Find the shaded part area?

Question

Two squares of side 5 and 2 respectively. They are touching each other. Diagonals of the square are joined. find the area of the shaded part?

Answer 1

Let measure of bases of small triangle be a, the small and big triangles are similar and we can write:

$\frac{a}{5}=\frac{2}{5+2}$ ⇒ $a=\frac{5\times 2}{7}=\frac{10}{7}$

So the area of small triangle is :

$A=(\frac{10}{7}\times 2)/2=\frac{10}{7} $

And shaded area is:

$2\times 2-\frac {10}{7}=\frac{18}{7}$

Answer 2

Hint: The triangles formed by joining the vertices of the squares as shown in the figure are similar.