﻿ Unit 9 Section 3 : Perimeter of Special Shapes

# Unit 9 Section 3 : Perimeter of Special Shapes

In this section we calculate the perimeters of various shapes. The perimeter of a circle is referred to as the 'circumference'.

The circumference, C, of a circle  =  2πr or πd where r is the radius and d is the diameter of the circle.

## Example 1

Calculate the circumference of a circle with radius 8 cm.

Using the formula, C = 2πr, gives
 C = 2 × π × 8  =  50.26548246 cm = 50.3 cm (to 3 significant figures)

## Example 2

The diagram shows a semicircle of diameter 12 cm.
Calculate the perimeter of the semicircle.

 Length of curve = π × 12 ÷ 2 = 18.84955592 cm
Straight edge  =  12 cm
 Total perimeter = 12 + 18.84955592 = 30.84955592 cm = 30.8 cm (to 3 significant figures)

## Example 3

The diagram shows a shape that is made up of a rectangle, a triangle and a semicircle.
Calculate its perimeter.

 Length of curve = π × 7 ÷ 2 = 10.99557429 cm
 Total perimeter = 8 + 5 + 8 + 7 + 10.99557429 = 38.99557429 cm = 39.0 cm (to 3 significant figures)

## Exercises

Question 1

Giving your answers correct to 3 significant figures, calculate the circumference of a circle with:

(a) (b) radius 6 m, m diameter 15 cm, cm radius 8 mm. mm
Question 2

Calculate the perimeter of each of the following shapes:

(a)

cm
(b)

cm
(c)

cm
(d)

cm
Question 3

Giving your answer correct to 3 significant figures, calculate the perimeter of the semicircle shown.

cm
Question 4

A circle of radius 8 cm is cut into four equal parts as shown in the diagram:

(a)

Calculate the circumference of the original circle, giving your answer correct to 2 decimal places.

cm
(b)

Calculate the perimeter of each of the 4 parts, giving your answers correct to 2 decimal places.

cm
Question 5

Calculate the perimeter of each of the following shapes, giving your answers correct to 1 decimal place. The circular parts are either semicircles or quarters of circles.

(a)

cm
(b)

cm
(c)

m
(d)

cm
Question 6

Calculate the perimeter of each of the following shapes:

(a)

cm
(b)

cm
Question 7

A square has an area of 36 m². Calculate its perimeter.

m
Question 8

Calculate the perimeter of this shape, giving your answer correct to the nearest centimetre:

m
Question 9

A circle of radius 32 cm is cut into 8 equal parts, as shown in the diagram.

Calculate the perimeter of each part, giving your answer correct to the nearest millimetre.

cm
Question 10

The total perimeter of a semicircle is 37 cm. Calculate the radius of the semicircle, giving your answer correct to the nearest millimetre.

cm
Question 11

The perimeter of this shape is 3t + 2s.

p = 3t + 2s

Write an expression for the perimeters of each of these shapes.
Write each expression in its simplest form.

(a)
p =
(b)
p =
(c)
p =
(d)
p =
Question 12

Each side of this hexagon is 1 cm long.

Write down the perimeter of the shaded shape.

cm
Question 13

Wyn and Jay are using their wheelchairs to measure distances.

(a)

The large wheel on Wyn's wheelchair has a diameter of 60 cm. Wyn pushes the wheel round exactly once. Calculate how far Wyn has moved.

Distance moved = cm (to one decimal place)
Distance moved = wheel circumference = π × 60 = 188.4955592 cm = 188.5 cm (to one decimal place)
(b)

The large wheel on Jay's wheelchair has a diameter of 52 cm. Jay moves her wheelchair forward 950 cm. Calculate how many times the large wheel goes round.

Number of turns = (to 3 significant figures)  or   complete turns

Wheel circumference = π × 52 = 163.362818 cm

Number of turns = 950 ÷ 163.362818 = 5.815276767 = 5.82 turns (to 3 s.f.) or 5 complete turns

Question 14

(a)

A circle has a radius of 15 cm. Calculate the area of the circle.

cm² (to 3 significant figures)
Area = π × 15² = 706.8583471 cm² = 707 cm² (to 3 s.f.)
(b)

A different circle has a circumference of 120 cm. What is the radius of the circle?

cm (to 3 significant figures)
Radius = 120 ÷ (2 × π) = 19.09859317 cm = 19.1 cm (to 3 s.f.)