Question

In the figure given below, $PQRS$ is a rectangle. Find the area of the shaded portion in the given figure.

• A. $180c{m}^2$
• B. $100c{m}^2$
• C. $280c{m}^2$
• D. $140c{m}^2$

Answer 1

The correct option is A $180c{m}^2$

R.E.F image

Given : PS = 10 cm ; SR = 28 cm

XR = 6 cm and RY = 20 cm

PQRS is a rectangle.

$\angle P=\angle Q=\angle R=\angle S={90}^{\circ }$

To find : Area of shaded region.

Area of shaded region = Area of rectangle - (Area of $△PSY$+Area of $△XRY$)

$=(28\times 10)c{m}^2-[\frac{1}{2}\times 8\times 10+\frac{1}{2}\times 20\times 6]c{m}^2$

$=280c{m}^2-\frac{200}{2}c{m}^2=280c{m}^2-100c{m}^2$

Area of shaded region $=180c{m}^2$