Math Class IV Perimeters PDF

# Chapter Five ## Perimeters of plane figures ### Introduction In this chapter, you will learn to find the perimeter of a rectangle, square and triangle. You will also learn to solve problems involving the concept of perimeters of plane figures. The competencies developed will be applied in buildin...

# Chapter Five ## Perimeters of plane figures ### Introduction In this chapter, you will learn to find the perimeter of a rectangle, square and triangle. You will also learn to solve problems involving the concept of perimeters of plane figures. The competencies developed will be applied in building constructions, estimating of distances covered and many other real-life applications. ### Think Mathematics without figures ### Concept of perimeter A perimeter is the length of the boundaries of a plane figure. Different ways are used to find the perimeter of a rectangle, square and triangle. The perimeter can be expressed in various metric units of length. ### The perimeter of a rectangle The perimeter of a rectangle is the sum of the lengths of its sides. ## Activity 1 Measuring the perimeter of a rectangle ### Steps 1. Put the 0 mark on a tape measure at one corner of the rectangle. 2. Measure the length of the rectangle's boundary until you reach the starting point. 3. Record the measurement of the length obtained. 4. Measure and record the length of each side of the rectangle using a ruler. 5. Add the lengths of all sides of the rectangle in step 4. 6. Compare the results from step 3 with those from step 5. 7. What is the perimeter of the rectangle. ## Activity 1 In Activity 1, the total length of the boundaries obtained is the perimeter of the rectangle. Thus, the perimeter of a rectangle is obtained by adding the lengths of all its four sides. ### The formula for finding the perimeter of a rectangle is given by; Perimeter of a rectangle = length + width + length + width = length + length + width + width = 2 x length + 2 x width Therefore, the perimeter of a rectangle = 2 x length + 2 x width. If l=length and w = width, then the perimeter will be; The perimeter of a rectangle = 2 x l + 2x w ## Example 1 Find the perimeter of the following rectangle. ### Solution Perimeter of the rectangle = length + width + length + width = 100 cm + 40 cm + 100 cm + 40 cm = 280 cm Or The rectangle has two sides with equal length and two sides with equal width. The perimeter is given by Perimeter of the rectangle = 2 x length + 2 x width =2 x 100 cm + 2 x 40 cm = 200 cm + 80 cm = 280 cm Therefore, the perimeter of the rectangle is 280 cm. ## Example 2 Find the perimeter of a rectangle of length 13 m and width 11 m. ### Solution Length = 13 m, width = 11 m Perimeter of a rectangle = 2 × length + 2 × width =2×13 m + 2x11m = 26 m + 22 m = 48 m Therefore, the perimeter of the rectangle is 48 m. ## Exercise 1 1. Measure the length of an exercise book and record it in centimetres. Also, measure the width of the same exercise book and record it in centimetres. > (a) Find the total length of all four sides of the exercise book. > (b) What does the length of four sides of the exercise book represent? 2. The classroom floor has a length of 20 metres and a width of 12 metres. Find its perimeter. 3. Find the perimeter of each of the following figures: > (a) > (b) > (d) ## The perimeter of a square The perimeter of a square is the sum of the lengths of all its sides. All sides of a square have equal length. Therefore, its perimeter can be found by multiplying the length of one side by 4. Thus, Perimeter of a saquare = length + length + length + length = 4 × length Therefore, the perimeter of a square = 4 × l. ## Example 1 Find the perimeter of the following square. ### Solution Perimeter of a square = length + length + length + length = 20 cm + 20 cm + 20 cm + 20 cm = 80 cm ### Alternative solution The square has four sides of equal length. It follows that, Perimeter of a square = 4 × length = 20 cm x 4 = 80 cm Therefore, the perimeter of the square is 80 cm. ## Example 2 The length of a square garden is 13 metres. Find its perimeter. ### Solution Length of the square garden = 13 m Perimeter of the garden = 4 × length = 4 x 13 m = 52 m Therefore, the perimeter of the garden is 52 m. ## Exercise 2 1. Find the perimeter of each of the following squares: > (a) > (b) > (d) 2. Find the perimeter of a square whose side has a length of 18 m. 3. The square has a side of 37 cm long. Find its perimeter. ## The perimeter of a triangle The perimeter of a triangle is the sum of the lengths of its three sides. Thus, the perimeter of a triangle is obtained by adding the lengths of its sides. ## Example 1 Find the perimeter of the following triangle. ### Solution Perimeter of a triangle = sum of the lengths of all sides = 6 cm + 7 cm + 9 cm = 22 cm Therefore, the perimeter of the triangle is 22 cm. ## Example 2 A triangle has sides measuring 14 metres, 16 metres and 11 metres. Find its perimeter. ### Solution Perimeter of a triangle = sum of the lengths of all sides =14m+16m+11m = 41 m Therefore, the perimeter of the triangle is 41 m. ## Exercise 3 1. Find the perimeter of each of the following triangles: > (a) > (b) > (c) 2. Find the perimeter of a triangle whose sides are 26 m, 24 m and 10 m. 3. A triangle has sides of lengths; 84 cm, 85 cm and 13 cm. Find its perimeter. ## Word problems involving perimeter Word problems involving perimeters are mathematical questions written in one or more sentence. The concept of perimeter is used to solve such real-life problems. ## Example 1 A square flower garden is 25 m long. Find its perimeter. ### Solution Length of the garden = 25 m. Perimeter of the garden = 25 m + 25 m + 25 m + 25 m = 100 m Therefore, the perimeter of the flower garden is 100 metres. ## Example 2 The football ground is 100 metres long and 64 metres wide. Find its perimeter. ### Solution Length of the football ground = 100 m Width of the football ground = 64 m The football ground has a rectangular shape as shown in the following figure. Perimeter of the ground = 2 × length + 2 x width = 2 x 100 m + 2 x 64 m = 200 m + 128 m = 328 m Therefore, the perimeter of the football ground is 328 m. ## Example 3 A pupil rode a bicycle a distance of 3 km from home to school. After school sessions, he went to the market to buy some fruits. The distance from the school to the market is 2 km. If the pupil used a short cut road to ride 1 km back home as shown in the following figure, what is the total distance covered? ### Solution The distance covered is the length of the entire route. This distance is given by the perimeter of the route. Perimeter of the route = distance from home to school + distance from school to the market + distance from the market to home = 3 km + 2 km + 1 km = 6 km Therefore, the pupil covered a distance of 6 km. ## Exercise 4 1. A teacher has a square shaped garden. If the garden has length of 20 metres, find its perimeter. 2. A triangular field has sides measuring 15 metres, 20 metres and 25 metres. Find the perimeter of the field. 3. A square table has a length of 8 metres. Find its perimeter. 4. Juma walked from his home to school. After school, he walked to the market, from the market to the hospital, and back home as shown in the following figure: ### Home ### School ### Hospital ### Market Find the total distance walked by Juma. ## Activity 2 ### Recognising perimeters of plane figures using reliable ICT resources ### Description Use online programs and computer packages such as GeoGebra and Khan Academy to learn more on perimeters of plane figures and their applications. ## Summary 1. Perimeter is the length of the boundary of a plane figure. 2. Perimeter of a rectangle = 2 × length + 2 × width. 3. Perimeter of a square = 4 × length. 4. Perimeter of a triangle = The sum of the lengths of all sides. ## Revision Exercise 1. Find the perimeter of each of the following figures. > (a) > (b) > (c) > (d) 2. The length of one side of a square is 23 cm. Find its perimeter. 3. A school garden is rectangular in shape. If its length is 1200 m and its width is 80 m, find its perimeter. 4. Find the perimeter of a triangle if each of its sides is 17 cm long. 5. Find the perimeter of a square whose side length is 16 m. 6. Jamila ran one round of a rectangular field of length 100 m and width 70 m. What is the total distance covered by Jamila? 7. Find the length of the rope that can be used to surround a window that is 3 m high and 2 m wide. 8. The perimeter of square A is 4 metres. Two same squares make a rectangle B. Baraka and Neema calculated the perimeter of the rectangle B. Baraka got a perimeter of 8 metres, while Neema got 6 metres. Who got the correct answer? Give reason for your answer. 9. A rectangular shed has a length of 28 metres and a width of 4 metres. Find its perimeter. 10. Furaha has a square garden of a side length of 7 m, he calculated its perimeter. What is the perimeter obtained by Furaha in centimetres? 11. Musa drew a rectangle with a length of 80 mm and a width of 50 mm. What is its perimeter in centimetres? 12. The tailor bought a piece of fabric with a length of 2 metres and a width of 1 metre. What is the perimeter of that piece of fabric in centimetres? 13. A carpet in the teachers' office is 7 metres long and 5 metres wide. Find its perimeter. 14. The garden has a triangular shape measured: 10 m, 7 m and 6 m. Find its perimeter. 15. Four pupils cut a piece of paper in a square shape. The piece of paper had a perimeter of 16 centimetres. If they cut the paper into four equal square pieces, what is the perimeter of each square.