Question

In the given figure, a circle is inscribed in a trapezium of height 14 cm and lengths of parallel sides are equal to 25 cm and 40 cm. What is the area of the shaded region?

Options

• 455 sq cm

• 154 sq cm

• 509 sq cm

• 301 sq cm

Answer 1

301 sq cm

Explanation:

Area of the shaded region = Area of the trapezium – area of the circle

Area of trapezium `=1/2 xx "height" xx "sum of parallel sides"`

`= 1/2 xx 14 xx (25 + 40) = 455  "sq cm"`

Area of the circle `= pi xx "r"^2= (22/7) ×7×7=154  "sq cm"`

Hence, area of the shaded region `= 455 - 154 = 301` sq cm