Area Problem

Geometry Level 1

In the diagram, A F = 21 , A E = 27 , B C = 30 , C D = 10 , A B ⊥ D F , A D ⊥ B E AF=21, AE=27, BC=30, CD=10, AB\bot DF, AD\bot BE .

Find the area of quadrilateral A B C D ABCD .


The answer is 510.

Albert Yiyi by albert yiyi , 31, Malaysia

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1 solution

Albert Yiyi
May 27, 2018

Insight: Area of triangle = 1 2 b h \frac{1}{2}bh

Connect A C AC .

S Δ A B C = 1 2 B C × A E = 405 S_{\Delta ABC} = \frac{1}{2}BC\times AE = 405

S Δ A D C = 1 2 C D × A F = 105 S_{\Delta ADC} = \frac{1}{2}CD\times AF = 105

S A B C D = 405 + 105 = 510 S_{ABCD} = 405 + 105 = 510

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