Question

Find the area of a trapezium ABCD in which AB$||$DC, AB$=77$cm, BC$=25$cm, CD$=60$cm and DA$=26$cm.

• A. $204c{m}^2$
• B. $1644c{m}^2$
• C. $1645c{m}^2$
• D. $1600c{m}^2$

Answer 1

The correct option is B $1644c{m}^2$

$Construction:$

Construct $DE$ such that $DE$ is parallel to $BC$

Now ,

Area of triangle $△ADE=\sqrt{s(s-a)(s-b)(s-c)}$

$s=\frac{26+25+17}{2}$

$⟹s=34$

Now, By putting the values we get,

Area of $△ADE=\sqrt{34(34-25)(34-26)(34-17)}$

$=\sqrt{34\times 9\times 8\times 17}$

$=204c{m}^2$

We also know that,

Area of $△ADE=\frac{1}{2}\times 17\times H$

By Equating this two areas we get,

$⟹\frac{1}{2}\times 17\times H=204$

$⟹H=\frac{204\times 2}{17}=24cm$

Now,

Area of Trapezium $ABCD=\frac{1}{2}\times (77+60)\times 24$

$=1644c{m}^2$