two lines are parallel

Geometry Level pending

Find the area of quadrilateral A B C D ABCD in square centimeters if B D = 2 41 cm BD=2\sqrt{41}~\text{cm} .


The answer is 70.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

By pythagorean theorem,

( B D ) 2 = ( C D ) 2 + ( B C ) 2 (BD)^2=(CD)^2+(BC)^2

( 2 41 ) 2 = 1 0 2 + ( B C ) 2 (2\sqrt{41})^2=10^2+(BC)^2

B C = 8 BC=8

The figure is a trapezoid, so the area is

A = 1 2 ( 6 + 8 ) ( 10 ) = 70 A=\dfrac{1}{2}(6+8)(10)=70 square centimeters

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