Question

The area of a trapezium is 64 cm and its height is 8 cm. If one of the parallel sides is
⅓
of the other, find the lengths of the two parallel sides.

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Answer 1

Given :

The area of a trapezium is 64 cm and its height is 8 cm. If one of the parallel sides is  ⅓  of the other

To Find :

Lengths of the two parallel sides

Solution :

Area of the trapezium is ,

$\sf \bigstar\ \; \pink{A=\dfrac{1}{2}\times (a+b)\times h}$

where ,

• a , b are parallel sides
• h denotes height

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Area of the trapezium = 64 cm²

Height = 8 cm

Let one parallel side be x

Other =  $\sf \dfrac{x}{3}$

$\to \sf 64=\dfrac{1}{2}\times (8)\times \bigg(x+\dfrac{x}{3}\bigg)\\\\\to \sf 64=4\times \bigg(\dfrac{4x}{3}\bigg)\\\\\to \sf 64=\dfrac{16x}{3}\\\\\to \sf 4=\dfrac{x}{3}\\\\\leadsto \sf \green{x=12\ cm}\ \; \bigstar$

One parallel side , x = 12 cm

Other parallel side , x/3 = 4 cm

Answer 2

Answer:

sum of its parallel sides = 16 sm

Step-by-step explanation:

Area of trapezium = 1 / 2 * h * ( p1 + p2)

or,                 64      = 1 / 2 * 8 * ( p1 + p2)

or,          ( p1 + p2)   = 16 cm

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