Question

The parallel sides of a trapezium are 25cm and 11 cm, while its nonparallel sides are 15 cm and 13 cm. Find the area of trapezium. Whoever will answer first and correctly with explanation will get 15 points plus will be marked brainliest.​

Answer 1

Given:

•parallel sides of a trapezium are 25cm and 11 cm

•nonparallel sides are 15 cm and 13 cm

To find:

area of trapezium ABCD

Construction:

Draw AE parallel to BC.

Proof:

AE ll BC and AB ll EC.

$\sf{\implies}$Quadrilateral ABCE is a parallelogram.

$\sf{\implies}$AE = 15cm

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Now, we will find the area of ∆ADE by Heron's Formula.

In ∆ADE,

a = 13, b = 14, c = 15.

$\sf{\implies}$s = 21

$\sf{ar(\triangle ADE)=\sqrt{s(s - a)(s - b)(s - c)} }$

$\sf{ar(\triangle ADE)= \sqrt{21(21- 13)(21 - 14)(21- 15)}}$

$\sf{ar(\triangle ADE)= \sqrt{21(8)(7)(6)}}$

$\sf{ar(\triangle ADE)=\sqrt{7056} }$

$\bf{ar(\triangle ADE)=84cm^2}$

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Let the height of the triangle be h.

$\sf{ar(\triangle ADE)=\frac{1}{2}\times base\times height}$

$\sf{\implies 84=\frac{1}{2}\times 14\times h}$

$\bf{\therefore h=12cm}$

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In parallelogram ABCE,

base = 11cm and height = 12cm

$\sf{area(ABCE)= base \times height}$

$\sf{\implies area(ABCE)=11\times 12}$

$\bf{\therefore area(ABCE)=132cm^2}$

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From figure,

area of trapezium ABCD = area of ∆ADE + area of parallelogram ABCE

$\sf{\implies}$area of trapezium ABCD = 84 + 132

$\boxed{\bf{\therefore area\: of\: trapezium\: ABCD = 216cm^2}}$

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@zaqwertyuioplm :)