# Find the shaded part area?

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?

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• Well, the slope of the diagonal is quite easy to calculate ... What have you tried? – Matti P. Jun 24 at 7:18
• I am new to geometry. I don't know how to proceed with this? – usmanharoon Jun 24 at 7:25
• I would start by calculating the height of the triangle that the diagonal makes with the smaller triangle. The slope of the diagonal is easy to calculate, it's $\frac{5}{5+2}= \frac{5}{7}$. What is then the height of the small triangle? When you know its height, you can calculate the area of the small triangle. Subtract that from the area of the small square, and you're done. – Matti P. Jun 24 at 7:26

## 2 Answers

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:

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

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