UKMT - Junior Mathematical Challenge - 2023 - 10 | Exact Science

10

In the diagram, all distances shown are in cm. The perimeter of the shape is 60 cm. What is the area, in cm², of the shape?

A. 192

B. 204

C. 212

D. 232

E. 252

Answer

A. 192

SOLUTIOn

Let the length of the right hand edge of the shape be h cm. Then 2(h + 18) = 60.

Therefore h = 12.So the area, in cm², of the shape is 18 × 12 − 6 × (12 − 8) = 216 − 6 × 4 = 216 − 24 = 192.

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