Mathematics
Grey Kangaroo
2022
8

8

Tony the gardener planted tulips and daisies in a square flowerbed of side-length 12 m, arranged as shown. What is the total area, in m2 , of the regions in which he planted daisies?

A 48 B 46 C 44 D 40 E 36

Answer

A

SOLUTIOn

First consider the intersection point of the lines forming the boundaries of the regions containing daisies. Since the arrangement of the regions is symmetric, these lines intersect at the mid-point of the flowerbed. Therefore, the diagonal passes through the intersection point. It divides the daisy beds into four congruent triangles, each of base 4 m and height 6 m as shown. Hence the total area of the regions in which daisies are grown is, in m2 , equal to 4 × 1/2 × 4 × 6 = 48.

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