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?

• A. 455 sq cm
• B. 154 sq cm
• C. 301 sq cm
• D. 509 sq cm

Answer 1

The correct option is C 301 sq cm

Area of the shaded region = Area of the trapezium - Area of the circle
Area of trapezium =$\frac{1}{2}\times height\times sumofparallelsides$
$=\frac{1}{2}\times 14\times (25+40)=455sqcm$
Area of the circle = $\pi \times r^2=\frac{22}{7}\times 7\times 7=154sqcm$
Hence, area of the shaded region = 455 - 154 = 301 sq cm.