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

455 sq cm

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365 sq cm

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301 sq cm

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482 sq cm

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Solution

The correct option is C 301 sq cm

Area of the shaded region = Area of the trapezium - Area of the circle
Area of trapezium = $\frac{1}{2} \times h e i g h t \times s u m o f p a r a l l e l s i d e s$
$= \frac{1}{2} \times 14 \times (25 + 40) = 455 s q c m$
Area of the circle = $π \times r^{2} = \frac{22}{7} \times 7 \times 7 = 154 s q c m$
Hence, area of the shaded region = 455 - 154 = 301 sq cm.

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

The correct option is C 301 sq cm Area of the shaded region = Area of the trapezium - Area of the circle Area of trapezium =12×height×sum of parallel sides =12×14×(25+40)=455 sq cm Area of the circle = π×r2=227×7×7=154 sq cm Hence, area of the shaded region = 455 - 154 = 301 sq cm.