The diagram shows a running track in the shape of a rectangle with two semicircular ends. The rectangle has length 80 m and width 40 m. 80 m 40 m © EAGLE BE...
Question 1 Report
The diagram shows a running track in the shape of a rectangle with two semicircular ends. The rectangle has length 80 m and width 40 m.
- Work out the total perimeter of the track. Give your answer correct to the nearest metre. (3)
- Work out the total area enclosed by the track. Give your answer correct to 3 significant figures. (2)
Answer Details
This question finds the perimeter and area of a composite shape made from a rectangle with two semicircular ends, where the two semicircles together form one full circle.
(a) The two semicircular ends, each of diameter 40 m, join to form one full circle, so their combined curved length is one full circumference: \[ \text{Circumference} = \pi \times 40 = 40\pi \] [1 mark]
The perimeter also includes the two straight sides of length 80 m each: \[ \text{Perimeter} = 2 \times 80 + 40\pi \] [1 mark]
\[ = 160 + 125.66\ldots = 286 \text{ m (nearest metre)} \] [1 mark]
(b) The enclosed area is the rectangle plus the full circle formed by the two semicircular ends (radius 20 m): \[ \text{Area} = 80 \times 40 + \pi \times 20^2 \] [1 mark]
\[ = 3200 + 1256.6\ldots = 4460 \text{ m}^2 \text{ (3 s.f.)} \] [1 mark]
Recognising that two semicircles of equal radius always combine into exactly one full circle avoids treating each end separately; it converts the track's curved boundary into a single circle calculation for both the perimeter and the area.
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