Chapter Fourteen Geometry PDF

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Fourteen Geometry Introduction In Standard Four, you learnt how to draw lines, line segmen...

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Fourteen Geometry Introduction In Standard Four, you learnt how to draw lines, line segments and rays. LY You also learnt how to find the perimeter of rectangles, squares and triangles. In this chapter, you will learnt about types of angles, how to draw angles, parallel lines and to distinguish between different types of N triangles and their properties. In addition, you will learn how to find the area of rectangles, squares and triangles. You will also learn how to O solve word problems related to lines, rectangles, squares, triangles and angles. Through this competence, you will acquire the knowledge about SE the properties of different shapes and their relationships to mapping and architecture. U Exercise 1: Revision Answer the following questions: E 1. Draw rays AB and BA. N 2. Find the perimeter of a rectangle with length 12 cm and width 8 cm. 3. Find the perimeter of a square with length 5 cm. LI 4. What is the difference between a square and a triangle? N 5. Draw a line segment XY. 6. Find the perimeter of each of the following figures: O (a) (b) R FO 7 cm 60 cm 60 cm \ 10 cm 70 cm 263 MATH std 5.indd 263 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE (c) (d) 14 cm 12 cm 24 cm 14 cm 16 cm LY 7. Find the perimeter of a rectangle of length 5 cm and width 3 cm. N 8. The perimeter of a square is 40 cm. What is the length of one of O its sides? Angles SE When two rays intersect, they form an angle. The unit used when measuring an angle is degree. A symbol “o” represents the degree of an angle. Consider U the following rays: A Ray AB B A Ray AC C E N When the rays AB and AC intersect, they form an angle as shown in the following figure: B LI N A O R C FO The angle formed by the intersection of the rays AB and AC is named as angle BAC or angle CAB. The notation ​∠BAC​or ​B​Â ​C​ represents the angle BAC. The symbol ​∠​or ˄ represents the word “angle”. 264 MATH std 5.indd 264 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE A vertex is a point where two rays meet or intersect. The plural for vertex is vertices. When naming an angle, the middle letter must be at the vertex. For example, letter A in ​B​Â ​C​is at the vertex A. Naming angles Example 1 LY Write in three different ways the angle given in the following figure: N P O Q SE R U The angle can be written in three different ways as follows: 1. Angle QPR or angle RPQ E 2. ​Q​P̂ ​R​or ​R​P̂ ​Q​. N 3. ∠ ​ QPR​or ​∠RPQ​ LI Example 2 N Write the names of all the angles which appear in the following figure: O P Q R FO R S U 265 MATH std 5.indd 265 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE The angles which appear in the drawing are: ​∠PRQ or ∠QRP, ∠PRS or ∠SRP, ∠SRUor ∠URS, and ∠QRU or ∠URQ.​ Exercise 2 Answer the following questions: 1. Write the names of each angle in the following figures: LY R W (a) (b) N M O X Y N (c) (d) SE A U E G B E N F C LI N 2. Mention the vertex in each of the following angles: Y S O (a) (b) R R FO X Z T 266 MATH std 5.indd 266 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE 3. Write the names of all angles in each of the following geometrical figures: (a) (b) A B J K LY D C L N 4. How many angles does each of the following figures have? (a) A triangle O (b) A square. Types of angles SE The following are the types of angles: U Acute angle An acute angle is an angle which is greater than 0 degrees (0°) and less than E 90 degrees (90°). Angle ABD in the following figure is between 0° and 90°, N thus it represents an acute angle. A LI N B O D R Right angle FO A right angle is an angle that measures exactly 90°. Angle WXY in the following figure is a right angle. 267 MATH std 5.indd 267 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE A right angle is greater than an acute angle and less than an obtuse angle. In geometrical figures, all right angles are denoted by. W X Y LY Obtuse angle An obtuse angle is an angle that measures between 90° and 180°. In the N following figure, angle GHI is an obtuse angle. O G H SE I An obtuse angle is greater than a right angle and less than a straight angle. U Straight angle A straight angle is an angle that measures exactly 180°. It is represented by a straight line. In the following figure, angle STU is a straight angle. E N S T U Reflex angle LI A reflex angle is an angle that is greater than 180° and less than 360°. In the following figure, ​∠MON​is a reflex angle. N O O R M N FO A reflex angle is greater than 180° and less than 360°. 268 MATH std 5.indd 268 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE Full angle A full angle is an angle that measures exactly 360°. It is greater than all other angles. The following figure represents a full angle. Exercise 3 LY Answer the following questions: N 1. Study carefully the following angles and then answer the questions that follow. O G A B C H SE H U E I L N N LI K W N O X Y M N R (a) Which angle is an acute angle? (b) Which angle is a right angle? FO (c) Mention an obtuse angle? (d) Which angle is a straight angle? (e) Which angle is a reflex angle? 269 MATH std 5.indd 269 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE 2. Name all the right angles in the following figure: P Q S R LY 3. Write “TRUE” or “FALSE” for each of the following statements: (a) An acute angle is less than a right angle. N (b) An obtuse angle is less than an acute angle. (c) Every straight angle equals the sum of two right angles. O (d) A reflex angle is less than an obtuse angle. (e) A straight angle is less than a reflex angle. SE 4. Name all the right angles in the following figure: U L M E N O N LI 5. Write the names and types of all the angles in the following figure. P N R O Q R S FO U 6. Name two geometrical figures whose inside angles are all right angles. 270 MATH std 5.indd 270 30/07/2021 14:50  FOR ONLINE USE ONLY Construction of angles by estimation DO NOT DUPLICATE If you understand the properties of an angle, you can construct it by estimating its value. Example 1 Construct an acute angle JKL. Solution LY Steps: 1. Draw a ray KL. 2. Draw a ray KJ starting from K to J to get the vertex K and estimate ​ N ∠​JKL such that it is less than 90°. 3. You get ​∠​JKL with vertex at K, as seen in the following figure. O J SE L U K E Example 2 N LI Construct a right angle ABC. N Solution Steps: A O 1. Draw a horizontal ray BC. 2. Draw a vertical ray BA starting from B R to a point A. The two rays form a right angle at the vertex B. FO 3. Insert a small square box at the vertex B C B as shown in the following figure: 271 MATH std 5.indd 271 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 4 Answer the following questions: 1. Construct ​∠​ABC and ​∠​DEF such that ​∠​ABC is smaller than ​∠​ DEF. 2. Construct a right angle LMN. 3. Construct an obtuse angle WXY. 4. Construct a straight angle ABC. 5. Construct an acute angle DEF. LY Lines of symmetry A line of symmetry is a line that divides a figure into two equal parts. Some N geometrical figures have infinite lines of symmetry, some have few lines O of symmetry and others have no lines of symmetry, especially figures with irregular shapes. SE Activity 1: Identifying lines of symmetry of a square U Steps: 1. Take a square shaped piece of paper. E N LI N 2. Fold the piece of paper into two equal parts as shown in the following O figure: R FO 272 MATH std 5.indd 272 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE 3. Unfold the paper. You will see the line of folding in the middle of the paper. This line is called line of symmetry. Line of symmetry LY 4. Fold the other sides of the square piece of paper. You will get lines of N symmetry as seen in the following figure: O SE Four lines of symmetry U Therefore, a square has four lines of symmetry. E N Activity 2: Identifying lines of symmetry of a rectangle LI Steps: 1. Take a piece of paper with the shape of a rectangle as shown in the N following figure: O R FO 273 MATH std 5.indd 273 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE 2. Fold the piece of paper to get two equal parts as shown in the following figure: LY 3. After unfolding the piece of paper, you will see a straight vertical line N in the middle of the paper as seen in the following figure: O Line of symmetry SE U 4. Fold again the folded piece of paper along its length through the centre. Unfold the piece of paper to get lines of symmetry as seen in the following figure: E N LI N O R FO Therefore, a rectangle has two lines of symmetry. 274 MATH std 5.indd 274 30/07/2021 14:50  FOR ONLINE USE ONLY Exercise 5 DO NOT DUPLICATE Answer the following questions: 1. Determine the number of lines of symmetry in each of the following figures: (a) (b) LY (c) (d) N O (e) (f) SE U E (g) N LI N 2. How many lines of symmetry do the following figures have? O (a) (b) R FO 275 MATH std 5.indd 275 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE 3. Find the number of the lines of symmetry in the following figures. (a) (b) LY N O 4. How many lines of symmetry does the following geometrical figure have? SE U E 5. How many lines of symmetry does the following figure have? N LI N O R 6. Draw a geometrical figure with a shape of number 8 and show its lines FO of symmetry. 276 MATH std 5.indd 276 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE 7. Copy the following figures and draw the lines of symmetry for each figure. (a) (b) (c) LY N Triangles O A triangle is a plane geometrical figure with three angles and three sides. B SE Side U A C E Angle N Types of triangles LI (a) Right angled triangle This is a type of a triangle with 90° among its three angles. Triangle VLM is N an example of a right angled triangle with ​∠VLM = ​90°.​​ ​​ O V R FO L M 277 MATH std 5.indd 277 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE The two sides, ​​‾ VL​​ and ‾ LM​​ ​​ are perpendicular. That is, they intersect at 90°. Also, right angled triangle has two acute angles LVM and VML. (b) Isosceles triangle It is a type of a triangle with two equal sides and two equal angles. The following figure is an example of an isosceles triangle. A LY N O B C ‾ In this triangle, the two sides AB ‾ ​​ ​​ and AC​​ ​​ are equal. Also, two of its angles, that is, ∠ ​ ABC​and ∠ SE ​ ACB​are equal. Isosceles triangles have one line of symmetry. (c) Equilateral triangle U This is a type of a triangle with all its sides equal and all its angles equal. The following figure is an example of an equilateral triangle. Y E N LI X Z N All sides of the triangle XYZ are equal, that is, ​​‾ XY​ = ​‾ XZ ​= ‾ YZ​​ ​. Also, all its O angles are equal, that is, ​∠XYZ = ∠YXZ = ∠XZY​. Equilateral triangle has three lines of symmetry. R (d) Obtuse angled triangle FO This is a triangle with one obtuse angle and two acute angles. Triangle DEF in the following figure is an example of an obtuse triangle. 278 MATH std 5.indd 278 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE K L M All the three sides and angles of an obtuse triangle are not equal. An obtuse triangle has no line of symmetry. LY Exercise 6 N Answer the following questions: O 1. List down the properties of a right angled triangle. 2. What is the difference between an equilateral triangle and an isosceles triangle? SE 3. Mention the types of triangles. U 4. How many vertices does an equilateral triangle have? E 5. Why is the following figure known as an isosceles triangle? C N LI N O A B R Areas of rectangles, squares and triangles The area of a geometrical figure is a space occupied by a flat shape or the FO surface of an object. The area can be calculated by subdividing the figure using equal square units and then count the squares. The area can also be obtained using proper derived formulas. 279 MATH std 5.indd 279 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE The area of a rectangle Activity 3: Finding the area of a rectangle by counting squares units Steps: 1. Draw a rectangle ABCD with a length of 8 square units and width of 6 LY square units on a graph paper. 2. Count the number of small squares in the rectangle ABCD. N 3. The number of square units is the area of the rectangle ABCD. O A B SE U E D C N LI N O Rectangle ABCD has 48 square units. So, the area of the rectangle is 48 square units. R FO 280 MATH std 5.indd 280 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 1 Finding the area of a rectangle by using formula and measurements. 8 cm 6 cm LY N Solution O The area ‘A’ of a rectangle of length L and width W is given by the product of its length and its width. That is, ​L × W​. SE The length is 8 cm and the width is 6 cm. The area of the rectangle ​=  length × width​ U = ​   8 cm × 6 cm​ ​A  =  48 square centimetres or 48 c​m​​ 2​ .​ E Therefore, the area of a rectangle is 48 cm2. N Example 2 LI (a) The area of a rectangle is 800 cm2. If the length of the rectangle is N 40 cm, find its width. O Solution The area is 800 cm2. R The length is 40 cm. FO ​A rea = length × width​ 8 ​ 00 cm = 40 cm × width​ 281 MATH std 5.indd 281 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE To get the width we divide Area by Length: 800 c ​m​​ 2​ _ 800 × cm × cm ___________ ​Width = ​   ​= ​        ​ ​ 40 cm 40 × cm 800 cm _ ​Width = ​   ​  = 20 cm​ 40 Therefore, the width of the rectangle is 20 cm. LY (b) The length of the cover page of a book is 30 cm and its width is 20 cm. Find the area of the cover page of the book. N Solution O The cover page of the book has the shape of a rectangle. The area of a rectangle = length × width Length = 30 cm Width = 20 cm SE ​ rea     = 30 cm × 20 cm A U               = 600 c​m​​ 2​​ Therefore, the area of the cover page of the book is ​600 c ​m​​ 2​​. E N Exercise 7 LI Answer the following questions: 1. Find the area of each of the following figures: N (a) (b) O 4m R 12 cm FO 20 m 5 cm 282 MATH std 5.indd 282 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE 30 cm (c) (d) 18 cm 45 cm 8 cm LY (e) (f) N 15 cm 17 cm O 21 cm 40 cm SE 2. Find the area of a rectangle of 10 cm length and 9 cm width. U 3. The area of a rectangle is 100 m2 and its width is 4 m. Find its length. 4. If a teacher’s table has a length of 80 cm and width of 60 cm. Find its E surface area. N 5. The area of the school farm is 820 m2. If its length is 41 m, what is its LI width? N 6. The floor of a classroom has a length of 7 m and a width of 6 m. Find O its area. 7. A rectangle has a length of 35 cm and a width of 26 cm. Find its area. R FO 8. A road has a length of 8 800 m and a width of 9 m. Find its surface area. 9. A rectangular garden measures 15 m by 330 m. What is its area? 283 MATH std 5.indd 283 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE 10. Find the area of a piece of paper of length 32 cm and width 20 cm. 11. The length of a rectangle is 215 metres. If its area is 19 780 square metres, find the width of the rectangle in centimetres. 12. Find the area of each of the following figures: 12 m (a) (b) LY 100 cm N 24 m 200 cm O SE (c) (d) 39 m U 27 cm 17 m E N 61 cm LI Area of a square N Activity 4: Finding the area of a square by counting square units O Steps: R 1. Construct a square EFGH having 7 horizontal and 7 vertical square FO units on a graph paper. 2. Count all the square units in the square EFGH. 284 MATH std 5.indd 284 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE 7 square units F E 7 square units LY H N G O SE 3. The number of square units equals the area of the square EFGH. 4. The square EFGH has 49 square units. Therefore, the area of the U square EFGH is 49 square units. E Example 1 N Finding the area of a square using a formula. LI 7 cm N O 7 cm R FO 285 MATH std 5.indd 285 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution The formula for calculating the area of a square is to multiply the lengths of two adjacent sides. ​Area of the square = length × length = 7 cm × 7 cm ​    = 49 cm​​ 2​​ LY Therefore, the area of the square is 49 cm2. N Example 2 O A window has a length of 70 cm and width of 70 cm. Find the area of the window. Solution SE 70 cm U E 70 cm N LI N The shape of the window is a square. One side has length 70 cm. O The adjacent side has length 70 cm. ​Area of the square = length × length R = 70 cm × 70 cm FO ​    = 4900 cm​​ 2​​ Therefore, the area of the window is 4 900 cm2. 286 MATH std 5.indd 286 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 3 Find the area of the following square. M N LY 18 m N P O 18 m O Solution A side of the above square has length m 18. ​Area of the square = length × length SE = 18 m × 18 m U ​    = 324 m​​ 2​​ Therefore, the area of the square is 324 m2. E N Example 4 LI The area of a square is 576 cm2. Find the length of one of its sides. N O Solution R Area = 576 cm2. Length of one side = ? FO 287 MATH std 5.indd 287 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE length × length = Area of a square = 576 cm2. length × length = 576 cm2 Length = 24 cm × 24 cm = 24 cm Therefore, the length of the square is 24 cm. LY N Exercise 8 O Answer the following questions: SE 1. A square has a side of length 40 cm. Find its area. 2. The area of a square garden is 441 square metres. What is the length U of the garden? 3. Find the area of a square region whose side has a length of 50 E centimetres. N 4. A square has an area 784 square centimetres. What is the length of LI its sides? N 5. The floor of a classroom is in the form of a square. If the length of one O of its sides is 9 metres, what is the area of the floor? 6. Find the area of each of the following figures: R FO 288 MATH std 5.indd 288 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE (a) (b) 8 cm 10 cm 8 cm 10 cm (c) (d) LY 11 cm 35 cm N O 11 cm 35 cm Area of a triangle SE Activity 5: Finding the area of a triangle by counting square units U L M E N LI N O O N R FO 289 MATH std 5.indd 289 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE Steps: 1. Construct the square LMNO on a graph paper having 6 square units by 6 square units. 2. Draw a straight line to join the points N and L to get two triangles LMN and LON. 3. Count the number of square units and the number of half square units in the triangle LON. LY Number of square units = 15. Number of half square units = 6. N But, 2 half square units are equal to 1 unit square. O Thus, the 6 half square units are equal to ​6 ÷ 2 = 3​ square units. The total number of square units in a triangle LON is ​15 + 3 = 18​. SE Therefore, the area of triangle LON is 18 square units. This area of triiangle LON is the same as the area of triangle LMN. U Example 1 E Find the area of triangle PQR by using a formula. N P LI N O 6 cm R R FO Q 8 cm 290 MATH std 5.indd 290 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution The area of a triangle is given by the formula _1 ​Area (A) =  ​   ​ base (b) × height (h)​. 2 1 _ That is, ​A = ​   ​ × b × h.​ 2 In the case of the above triangle, b = 8 cm LY h = 6 cm 1 _ ​Area =  ​   ​  × 8 cm × 6cm N 2 48 _ =  ​   ​ ​cm​​  2​  O 2 ​    = 24 cm​​ 2​ ​ SE Therefore, the area of the triangle PQR is 24 cm2. U Example 2 Find the area of a triangle whose height is 10 m and whose base is 15 m. E Solution N h = 10 m LI b = 15 m 1 N _ ​A =  ​   ​ × b × h 2 O 1 _ =  ​   ​  × 15 m × 10 m 2 R 150 2 _ =  ​   ​  ​  m​​  ​ 2 FO ​ = 75 m​​ 2​ ​ Therefore, the area of the triangle is 75 m2. 291 MATH std 5.indd 291 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 3 (a) Calculate the area of the triangle KLM. L 12 cm LY K N M N Solution 26 cm The base is KM = 26 cm O The height is LN = 12 cm 1 _ ​A =  ​   ​  × b × h 2 1 _ SE =  ​   ​  × 26 cm × 12 cm 2 U 312 _ = ​   ​  ​  cm​​  2​ 2 E ​ = 156 cm​​ 2​ ​ N Therefore, the area of the triangle KLM is 156 cm2. LI (b) Find the area of the triangle RST. T N O 20 m R FO R S 9m 292 MATH std 5.indd 292 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution _1 ​Area of triangle = ​   ​ × base × height​ 2 The base is the line RS whose length is 9 cm. The height is the line ST whose length is 20 cm. 1 _ ​Area =  ​   ​ × 9 m × 20 m 2 LY 180 _ =  ​   ​​m​​  2​ 2 N ​       = 90 m​​ 2​​ Therefore, the area of triangle RST is 90 m2. O (c) The area of a certain triangle is 225 m2. If it has a base of 30 m, find its height. SE Solution 1 U _ ​Area of a triangle =  ​   ​ × base × height​ 2 Area = 225 m Base = 30 m E 1 _ N ​​225 m​​  2​ =  ​   ​  × 30m × h 2 LI ​225 m​​  2​ = 15m × h N 225 × m × m _ h =  ​   ​ 15 m O 225 m _ =  ​   ​ 15 R = 15 m.​ FO Therefore, the height of the triangle is 15 m. 293 MATH std 5.indd 293 30/07/2021 14:50  FOR ONLINE USE ONLY Exercise 9 DO NOT DUPLICATE Answer the following questions: 1. Calculate the area of each of the following geometrical figures: A P (a) (b) 3 cm 8 cm LY Q 4 cm R C 6 cm B N (c) (d) Y K O 7 cm M 12 cm L SE X 20 cm Z 10 cm U Z 24 cm (e) (f)L B 19 cm E 14 cm N M LI D 48 cm C N (g) (h) M O R 10 cm S 20 cm R 10 cm 5 cm N FO T L 294 MATH std 5.indd 294 30/07/2021 14:50 m 24 m 24 m 24  FOR ONLINE USE ONLY DO NOT DUPLICATE 2. Find the area of a triangle with a height of 16 metres and a base of 19 metres. 3. A triangle whose height is 30 cm has an area of 600 cm2. Find of base. 4. A triangle has an area of 195 square metres. If it has a base of 26 metres, what is its height? LY Exercise 10 N Answer the following questions: O 1. List five types of angles. SE 2. How many right angles are in a straight angle? 3. What is the smallest angle among the five types of angles? U 4. Give the properties of a reflex angle. E 5. Give the properties of an equilateral triangle. N 6. Write the type of triangle which has one right angle and two acute angles. LI 7. Write the formula for calculating the area of a rectangle. N O 8. Calculate the area of the following geometrical figure: R 23 cm FO 23 cm 295 MATH std 5.indd 295 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE 9. The area of a square is 900 square centimetres. Calculate the length of its sides. 10. A square has a side of length 41 centimetres. Find its area. 11. Calculate the area of the following geometrical figure. LY 3 cm 7 cm 3 cm N 4 cm 14 cm O SE 12. The area of a triangle is 1 485 square centimetres. If its base is 66 U centimetres, find its height. 13. A triangle has a height of 25 metres and a base of 32 metres. Calculate E its area. N 14. Find the area of the geometrical figure PQR. LI N O 12 cm R 32 cm FO 15. Calculate the area of the following square: 296 MATH std 5.indd 296 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE 61 m LY 16. A rectangle RSTU has a length of 18 centimetres and a width of 14 N centimetres. Find the area of the rectangle. O 17. The area of a rectangle is 1 134 square centimetres. If it has a length of 42 centimetres, calculate its width. SE 18. The area of a triangle is 372 square centimetres. If it has a height of 24 centimetres, find its base. U 19. A rectangle has a length of 37 centimetres and a width of 27 centimetres. Calculate the area of the rectangle. E N 20. Calculate the area of a triangle with a base of 70 cm and a height of 84 cm. LI Summary N O 1. An angle is formed when two straight lines meet at a point. 2. A vertex is the point where two straight lines meet. R 3. The height of a triangle can be measured inside or outside the triangle. 4. The formula for calculating the area of a rectangle is length × width. FO _1 5. The formula for calculating the area of a triangle is ​ ​   ​ ​× base × height. 2 6. The formula for calculating the area of a square is length × length. 297 MATH std 5.indd 297 30/07/2021 14:50