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CAT 2022 Slot 1 QA Question & Solution

GeometryMedium

Question

A trapezium $ABCD$ has side $AD$ parallel to $BC, \angle BAD = 90^\circ, BC = 3$ cm and $AD= 8$ cm. If the perimeter of this trapezium is 36 cm, then its area, in sq. cm, is

Solution

Question Figure

CD = $\sqrt{\ y^2+25}$

$11+y+\sqrt{y^2+25}=36$

$\sqrt{y^2+25}=25-y$

$y^2+25=25^2+y^2-50y$

2y = 24

y = 12

Area of trapezium = $3y+\frac{5y}{2}=\frac{11y}{2}=\frac{11}{2}\left(12\right)=66$