Mathematics
ABCD is a quadrilateral. If AL ⊥ BD and CM ⊥ BD, prove that : ar (quad.ABCD) = × BD × (AL + CM).
Theorems on Area
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Answer
We know that,
Area of triangle = × Base × Height
Area of triangle ABD = × BD × AL
Area of triangle CBD = × BD × CM
We know that,
Area of quadrilateral ABCD = Area of △ ABD + Area of △ CBD
= × BD × AL + × BD × CM
= × BD × (AL + CM).
Hence, proved that ar (quad. ABCD) = × BD × (AL + CM).
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