Question

The area of a trapezium is 165 cm² and its height is 10 cm. If one of the parallel sides is double of the other, find the two parallel sides. 

Answer 1

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Let one side of trapezium is x, then other side parallel to it = 2x 

Area of trapezium = 165 cm²

Height of trapezium = 10 cm

Now, area of trapezium = 1/2 (p₁ + p₂) × h

⇒ 165 = 1/2(x₁ + 2x) × 10 

⇒ 165 = 3x × 5 

⇒ 165 = 15x

⇒ x = 165/15 

⇒ x = 11

Therefore, 2x = 2 × 11 = 22

Therefore, the two parallel sides are of length 11 cm and 22 cm. 
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Answer 2

The two two parallel sides of trapezium is 11 cm and 22 cm

Trapezium

A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other.

Area of trapezium

Area of trapezium is given by :

A $=1 / 2\left(p_{1}+p_{2}\right) \times h$

Consider  one side of trapezium is $x$, and the other side parallel to it is  $=2 x$

Given:

Area of trapezium $=165 \mathrm{~cm}^{2}$

Height of trapezium $=10 \mathrm{~cm}$

Step by step solution

Substitute the values in  given equation

$=1 / 2\left(p_{1}+p_{2}\right) \times h$

$&\Rightarrow 165=1 / 2\left(x_{1}+2 x\right) \times 10 \\&\Rightarrow 165=3 x \times 5 \\&\Rightarrow 165=15 x \\&\Rightarrow x=165 / 15 \\&\Rightarrow x=11$

so, $2 x=2 \times 11=22$

Hence the two parallel  sides of trapezium is given by $11$cm and $22$ cm

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