Mensuration: Perimeter of a Rectangle

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Questions and Answers

What is the perimeter of a closed figure?

  • The longest side of the figure.
  • The volume occupied by the figure.
  • The area enclosed by the figure.
  • The sum of the lengths of all the sides of the figure. (correct)

The perimeter of a shape can only be calculated for regular polygons.

False (B)

Explain how the concept of perimeter might be useful for someone planning to install a fence around their backyard.

To determine the extent of the fence material required.

Perimeter is the distance covered along the boundary forming a ______ figure when you go round the figure once.

<p>closed</p> Signup and view all the answers

A rectangular garden is 20 meters long and 10 meters wide. What is its perimeter?

<p>60 meters (C)</p> Signup and view all the answers

Which of the following professions would MOST likely use the concept of perimeter in their day-to-day work?

<p>A construction worker building a fence (A)</p> Signup and view all the answers

Describe a real-world application of perimeter beyond fencing or building walls.

<p>Determining the length of trim needed around a window or door.</p> Signup and view all the answers

Match the shape with the correct method to calculate its perimeter:

<p>Triangle = Add the lengths of its three sides. Rectangle = Multiply 2 by the sum of its length and width. Regular Pentagon = Multiply the length of one side by 5. Irregular Polygon = Add the length of all sides</p> Signup and view all the answers

Which of the following statements accurately describes the relationship between the area and perimeter of a rectangle?

<p>For a given area, the rectangle with the least perimeter is always a square. (C)</p> Signup and view all the answers

The perimeter of an equilateral triangle is calculated by multiplying the length of one of its sides by 4.

<p>False (B)</p> Signup and view all the answers

A rectangle has a length of 8 units and a breadth of 5 units. What is its perimeter?

<p>26 units</p> Signup and view all the answers

Figures in which all sides and angles are equal are called ________ closed figures.

<p>regular</p> Signup and view all the answers

Match the formula with the correct shape:

<p>Area of a square = side × side Perimeter of a rectangle = 2 × (length + breadth) Perimeter of a square = 4 × length of its side Area of a rectangle = length × breadth</p> Signup and view all the answers

A rectangle has a length of 12 cm and a breadth of 5 cm. What is its area?

<p>60 sq cm (A)</p> Signup and view all the answers

The area of a square with a side of 7 cm is 49 sq cm.

<p>True (A)</p> Signup and view all the answers

A rectangular garden is 8 m long and has an area of 56 sq m. What is the width of the garden?

<p>7 m</p> Signup and view all the answers

The area of a rectangle is found by multiplying its ______ by its breadth.

<p>length</p> Signup and view all the answers

If a square has an area of 81 sq m, what is the length of one of its sides?

<p>9 m (D)</p> Signup and view all the answers

To find the area of an irregular shape on a grid, you only count the fully filled squares.

<p>False (B)</p> Signup and view all the answers

A room is 5 m long and 4 m wide. What is the area of the floor?

<p>20 sq m</p> Signup and view all the answers

The area of a square is calculated by multiplying the side by ______.

<p>itself</p> Signup and view all the answers

How many tiles of size 0.5 m x 0.5 m are needed to cover a floor of 4 m x 3 m?

<p>48 (D)</p> Signup and view all the answers

A rectangle with sides 3 cm and 4 cm has the same area as a square with sides of 6 cm.

<p>False (B)</p> Signup and view all the answers

The area of a rectangular piece of cardboard is 48 sq cm, and its width is 6 cm. What is the length?

<p>8 cm</p> Signup and view all the answers

The area of a square with a side of 9 m is ______ sq m.

<p>81</p> Signup and view all the answers

Match the shape with its corresponding area calculation:

<p>Rectangle = Length × Breadth Square = Side × Side</p> Signup and view all the answers

A piece of cloth is 2 m long and 1.5 m wide. What is its area?

<p>3 sq m (B)</p> Signup and view all the answers

When finding the area of a floor covered by a carpet, the area not covered by the carpet is found by adding the area of the floor to the area of the carpet.

<p>False (B)</p> Signup and view all the answers

A rectangular garden is 20 meters long and 10 meters wide. What is the perimeter of the garden?

<p>60 meters (A)</p> Signup and view all the answers

The perimeter of a rectangle is found by adding the length and breadth together.

<p>False (B)</p> Signup and view all the answers

What is the formula for the perimeter of a regular hexagon, where 's' represents the length of one side?

<p>6s</p> Signup and view all the answers

The perimeter of a square is equal to 4 times the length of its ________.

<p>side</p> Signup and view all the answers

Match the regular shape with the formula to calculate its perimeter:

<p>Equilateral Triangle = 3 × length of a side Square = 4 × length of a side Regular Pentagon = 5 × length of a side Regular Octagon = 8 × length of a side</p> Signup and view all the answers

If the perimeter of a square is 36 cm, what is the length of each side?

<p>9 cm (D)</p> Signup and view all the answers

A regular pentagon has 6 equal sides.

<p>False (B)</p> Signup and view all the answers

A farmer needs to fence a rectangular field that is 100m long and 50m wide. What length of fencing is required?

<p>300m</p> Signup and view all the answers

The perimeter of an equilateral triangle with sides of 7 cm is _______ cm.

<p>21</p> Signup and view all the answers

An athlete runs 5 laps around a rectangular park that is 60 m long and 40 m wide. What is the total distance the athlete runs?

<p>2000 m (A)</p> Signup and view all the answers

Converting all measurements to the same unit is not important when calculating perimeter.

<p>False (B)</p> Signup and view all the answers

What is the perimeter of a rectangle with a length of 8 cm and a width of 5 cm?

<p>26 cm</p> Signup and view all the answers

If the length of a rectangle is 12 cm and its perimeter is 40 cm, then its breadth is _______ cm.

<p>8</p> Signup and view all the answers

A square field has a side length of 50 meters. What is the cost to fence the field if fencing costs $10 per meter?

<p>$2000 (B)</p> Signup and view all the answers

The perimeter of a shape is the area it covers.

<p>False (B)</p> Signup and view all the answers

A rectangular park has a length of 150 m and a breadth of 100 m. If a person runs 3 complete rounds of the park, how much distance will they cover?

<p>1500 m (D)</p> Signup and view all the answers

The perimeter of a regular octagon with sides of 5 cm each is 45 cm.

<p>False (B)</p> Signup and view all the answers

The amount of surface enclosed by a closed figure is called its ______.

<p>area</p> Signup and view all the answers

Match the following shapes with the formulas to calculate their perimeters.

<p>Square = 4 × length of a side Rectangle = 2 × (length + breadth) Equilateral Triangle = 3 × length of a side Regular Pentagon = 5 × length of a side</p> Signup and view all the answers

A farmer wants to fence a rectangular field that is 120 m long and 80 m wide using 3 rows of wire. What is the total length of wire needed?

<p>1200 m (D)</p> Signup and view all the answers

To find the perimeter of an irregular polygon, you must measure the length of each side and add them together.

<p>True (A)</p> Signup and view all the answers

The perimeter of a regular hexagon is 42 cm. What is the length of each side?

<p>7 cm</p> Signup and view all the answers

When estimating area by counting squares on a grid, if more than half of a square is within the figure, you count it as ______ square.

<p>one</p> Signup and view all the answers

What is the perimeter of an isosceles triangle with two sides equal to 7 cm each and a third side of 5 cm?

<p>19 cm (B)</p> Signup and view all the answers

A square and a rectangle can have the same perimeter, even if their areas are different.

<p>True (A)</p> Signup and view all the answers

A piece of string 60 cm long is used to form an equilateral triangle. How long is each side of the triangle?

<p>20 cm</p> Signup and view all the answers

To find the perimeter of a rectangle, you can use the formula: 2 × (length + ______).

<p>breadth</p> Signup and view all the answers

Avneet arranges nine square paving slabs, each with a side of 0.5 m, in the form of a larger square. What is the perimeter of this arrangement?

<p>6 m (D)</p> Signup and view all the answers

Consider a shape drawn on a grid paper where each square is 1 cm x 1 cm. The shape covers 10 full squares, 5 half squares and has 3 squares that are more than half filled. Approximately what is the area of the shape?

<p>14.5 sq cm (D)</p> Signup and view all the answers

Flashcards

Perimeter

The distance around a closed two-dimensional shape.

Perimeter of a polygon

The sum of all the side lengths of a shape.

Meera's Park Round

The distance covered by Meera around the park.

Perimeter of Meera's park

The park is 150 m long and 80 m wide, so the perimeter is 2(150 m + 80 m) = 460 m

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What is the perimeter of any closed figure?

Add the length of each of its sides

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How to calculate the perimeter of a rectangle?

AB + BC + CD + DA

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How to calculate the perimeter of a figure with 6 sides?

AB + BC + CD + DE + EF + FA

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How to calculate the perimeter of a figure with 12 sides?

AB + BC + CD + DE + EF + FG + GH + HI + IJ + JK + KL + LA

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Rectangle

A four-sided shape with opposite sides equal and all angles 90 degrees.

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Perimeter of a Rectangle Formula

Perimeter = 2 × (length + breadth)

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Square

A quadrilateral with all four sides equal in length and all angles 90 degrees.

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Perimeter of a Square Formula

Perimeter = 4 × length of a side

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Equilateral Triangle

A three-sided polygon with all sides equal in length and all angles equal.

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Perimeter of an Equilateral Triangle Formula

Perimeter = 3 × length of a side

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Regular Closed Figures

Closed figures with all sides and all angles of equal measure.

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Regular Pentagon

A polygon with five equal sides.

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Perimeter of a Regular Pentagon Formula

Perimeter = 5 × length of one side

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Regular Hexagon

A polygon with six equal sides.

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Perimeter of a Regular Hexagon Formula

Perimeter = 6 × length of one side

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Regular Octagon

A polygon with eight equal sides.

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Perimeter of a Regular Octagon Formula

Perimeter = 8 × length of one side

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Area

The amount of space inside a two-dimensional shape.

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Rectangle Perimeter

Perimeter = 2 × (length + breadth).

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Square Perimeter

Perimeter = 4 × length of a side.

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Equilateral Triangle Perimeter

Perimeter = 3 × length of a side.

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Perimeter of a Triangle

Sum of all sides of the triangle.

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Perimeter of Square

4 × length of one side

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Perimeter of Rectangle

2 × (length + breadth)

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Regular Polygon

A polygon with all sides equal length.

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Perimeter of Regular Polygon

Number of sides × length of one side

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Square Unit

Unit for measuring area; e.g., cm², m²

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Area Rule: More Than Half

Count as one square if more than half is in the region.

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Area Rule: Less Than Half

Ignore the section of area when estimating area on a grid.

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Area Rule: Exactly Half

Count half the square when estimating area on a grid.

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Isosceles Triangle

A triangle with two sides of equal length.

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What is Area?

Area is the measure of the amount of surface covered by a shape.

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How to Estimate Area?

Estimate area by counting fully-filled, half-filled, more than half-filled, and less than half-filled squares on a grid.

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Area of a Rectangle

Area of a rectangle is found by multiplying its length and breadth.

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Area of a Square

The area of a square is found by multiplying the length of one of its sides by itself.

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Finding Width of Rectangle

To find the width of a rectangle, divide the area by the length.

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Number of Tiles Needed

To find the number of tiles needed, divide the total area to be covered by the area of one tile.

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Units Consistency

Always ensure that the units of length and width are the same before calculating the area.

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Area of Irregular Shapes

To calculate the area of irregular shapes, divide them into rectangles and sum the areas.

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Units of Area

Area is measured in square units (e.g., sq cm, sq m).

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cm to meters

Converting cm to meters involves dividing by 100 (since 1m = 100cm)

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meters to cm

Converting meters to cm involves multiplying by 100 (since 1m = 100cm)

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Area Measurement

Area is always measured in square units.

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Perimeter Origin

The word perimeter come from the Greek word 'peri' meaning around and 'meter' meaning measure

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Composite Figure

A composite figure is made of two or more shapes

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Study Notes

  • Mensuration involves measuring the regions and boundaries of plane figures to compare them.

Perimeter

  • Perimeter refers to the distance around a closed figure.
  • It represents the length of wire or string needed to form the figure.
  • Perimeter has practical applications such as fencing a field, building a compound wall, or preparing a sports track.
  • Perimeter is found by summing the lengths of all sides of the closed figure.

Perimeter of a Rectangle

  • Perimeter of a rectangle = 2 × (length + breadth)
  • Example: A rectangular table cover that is 3 m long and 2 m wide requires 10 m of lace for the border.

Applications of Perimeter

  • An athlete running 10 rounds of a rectangular park that is 50 m long and 25 m wide covers 1500 m.
  • Fencing a rectangular field that is 240 m long and 180 m wide with 3 rounds of rope requires 2520 m of rope.
  • The cost of fencing a rectangular park that is 250 m long and 175 m wide at a rate of 12 per meter is 10200.

Perimeter of Regular Shapes

  • Regular closed figures have all sides and angles equal (e.g., squares and equilateral triangles).
  • Perimeter of a square = 4 × length of a side
  • Perimeter of an equilateral triangle = 3 × length of a side
  • Perimeter of a regular pentagon = 5 × length of a side
  • Perimeter of a regular hexagon = 6 × length of a side

Examples of Perimeter of Regular Shapes

  • Shaina travels 840 m by taking three rounds of a square park with a side of 70 m.
  • Pinky runs around a square field of side 75 m, covering 300 m, while Bob runs around a rectangular field with length 160 m and breadth 105 m, covering 530 m; Bob covers 230 m more than Pinky.
  • The perimeter of a regular hexagon is 18 cm and length of each side is 3 cm.

Area

  • Area refers to the amount of surface enclosed by a closed figure.
  • Area is measured in square units (e.g., sq cm, sq m).

Calculating Area Using Squared Paper

  • Count the number of squares enclosed by the figure.
  • Full squares are counted as 1 sq unit.
  • Ignore portions less than half a square.
  • More than half a square counts as one square.
  • Exactly half a square counts as 1/2 sq unit.

Area of a Rectangle

  • Area of a rectangle = length × breadth

Area of a Square

  • Area of a square = side × side

Examples of Area Calculations

  • A rectangle with length 12 cm and breadth 4 cm has an area of 48 sq cm.
  • The cost of tiling a rectangular plot of land that is 500 m long and 200 m wide at the rate of 8 per hundred sq m is 8000
  • A room that is 4 m long and 3 m 50 cm wide requires 14 square meters of carpet to cover the floor.
  • Covering the floor of a room that is 3 m wide and 4 m long with square tiles that are 0.5 m per side requires 48 tiles.

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