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) radius 6 m, m
(b) diameter 15 cm, cm
(c) 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.

The shaded shape below is made from 7 hexagon tiles.
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.)