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Area of Trapezium by Finding the Area of a Triangle of Same Area

The area of a...

Question

The area of a trapezium is 91 $c m^{2}$ and its height is 7 cm.If one of the parallel sides is longer than the other by 8 cm,find the two parallel sides.

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Solution

Area of trapezium=91 $c m^{2}$

Height(h)=7~cm

$∴ S u m o f p a r a l l e l s i d e s = \frac{A r e a \times 2}{h e i g h t} = \frac{91 \times 2}{7} = 26 c m L e t s h o r t e r s i d e = x t h e n l o n g e r s i d e = x + 8 ∴ x + x + 8 = 26 \Rightarrow 2 x = 26 - 8 = 18 \Rightarrow x = \frac{18}{2} = 9 ∴ O n e p a r a l l e l s i d e = 9 c m a n d s e c o n d s i d e = 9 + 8 = 17 c m H e n c e p a r a l l e l s i d e s a r e 17 c m, 9 c m$

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