8. Tony the gardener planted tulips and daisies in a square flowerbed of side-length $12 \mathrm{~m}$, arranged as shown. What is the total area, in $\mathrm{m}^{2}$, of the regions in which he planted daisies?
A 48
B 46
C 44
D 40
E 36
SOLUTION
$\mathbf{A}$

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 $4 \mathrm{~m}$ and height $6 \mathrm{~m}$ as shown. Hence the total area of the regions in which daisies are grown is, in $\mathrm{m}^{2}$, equal to $4 \times \frac{1}{2} \times 4 \times 6=48$.