7. Five squares and two right-angled triangles are positioned as shown. The areas of three squares are $3 \mathrm{~m}^{2}, 7 \mathrm{~m}^{2}$ and $22 \mathrm{~m}^{2}$ as shown.
What is the area, in $\mathrm{m}^{2}$, of the square with the question mark?
A 18
B 19
C 20
D 21
E 22
SolUTion
A

Notice that the central square shares an edge with both of the right-angled triangles and in each case the shared side is the hypotenuse of the triangle. By Pythagoras' Theorem, the area of the central square is equal to the sum of the areas of the squares on the shorter sides. By considering the triangle on the left we see the area, in $\mathrm{m}^{2}$, of the central square is $22+3=25$. Then, by considering the triangle on the right we see that the unknown area, in $\mathrm{m}^{2}$, is $25-7=18$.