Two parallel sides of a trapezium are 29\,{cm} and 21\,{cm}. Non-parallel sides are equal and each is of length 8.5\,{cm}. What is the area of the trapezium?

Correct Answer is : 187⋅5187 · 5187⋅5 square cm\,{cm}cm

Correct Answer is : 187⋅5187 · 5187⋅5 square cm\,{cm}cm

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UPSC CDS 2 2022 Math Paper

Question : 14 of 100

Marks: +1, -0

29\,\text{cm}

21\,\text{cm}

8.5\,\text{cm}

Solution: 👈: Video Solution

Area of trapezium

=\frac{1}{2}\times

sum of parallel sides

\times

height

\triangle \text{AED}

, by Pythagoras theorem,

\Rightarrow AD^2 = AE^2 + DE^2

\Rightarrow (8.5)^2 = (4)^2 + DE^2

\Rightarrow 72.25 = 16 + DE^2

\Rightarrow DE^2 = 56.25

\Rightarrow DE = 7.5\,\text{cm}

Area of trapezium

=\frac{1}{2}\times

sum of parallel sides

\times

height

\Rightarrow A = \frac{1}{2}(29+21) \times 7.5\,\text{cm}^2

\Rightarrow A = \frac{1}{2} \times 50 \times 7.5\,\text{cm}^2

\Rightarrow A = 187.5\,\text{cm}^2

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