Question

find the are of the shaded region

Answer 1

$\sf \Large Solution!!$

To find the area of the shaded portion, we have to find the area of the square ABCD. Then we have to find the area of the two triangles and add them. The added area of the two triangles have to be subtracted from the area of the square. We will get the area of the shaded portion.

Side of the square = 26 cm

Area of the Square = (Side)²

Area of the Square = (26 cm)²

Area of the Square = 676 cm²

Now, we find out the area of ∆EAF.

EA = 16 cm

AF = 8 cm

As we know, all the angles of the square are 90°, so we can say that this is a right angled triangle. We know the base and perpendicular side of the triangle. We can easily find out the area of this triangle.

Base = AF = 8 cm

Perpendicular = EA = 16 cm

Area = $\sf \dfrac{1}{2}\times Base\times Perpendicular$

Area = $\sf \dfrac{1}{2}\times 8\:cm\times 16\:cm$

Area = 64 cm²

Similarly, we can find out the area of the other triangle.

Base = BE = 10 cm

Perpendicular = 18 cm

Area = $\sf \dfrac{1}{2}\times Base\times Perpendicular$

Area = $\sf \dfrac{1}{2}\times 10\:cm\times 18\:cm$

Area = 90 cm²

Adding the areas of both the triangles.

64 cm² + 90 cm²

154 cm²

154 cm² is the area of the unshaded portion. We know the area of the whole figure which is square. Now, we will subtract the area of square and the added area of the triangles to get the area of shaded portion.

Area of square - Added area of both triangles = Area of the shaded portion

676 cm² - 154 cm² = Area of the shaded portion

Area of the shaded portion = 522 cm²