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
A
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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