Question

Determine the area of the shaded triangle inside the square explain your strategy

Answer 1

To find the area of the shaded region, we have to find the area of the square first.

`A_{\text{square}}=l^2=(10in)^2=100in^2`

Then, we find the area of each yellow triangle inside (up and down). The base of each triangle is 10 inches, and the height of each of them is 7 inches.

`\begin{gathered} A_{\text{triangle}}=(1)/(2)bh=(1)/(2)\cdot10in\cdot7in=35in^2 \\ A_{\text{triangle}}=(1)/(2)\cdot10in\cdot7in=35in^2 \end{gathered}`

Add the area of both triangles.

`A_t=35in^2+35in^2=70in^2`

At last, subtract the area of the triangles from the area of the square.

`A_{\text{shaded}}=100in^2-70in^2=30in^2`

Therefore, the area of the shaded region is 30 in^2.

The strategy is to subtract the area of the yellow triangles (up and down) from the area of the square.