In the given figure, $A B C D$ is a quadrilateral in which $A C = 24 c m, B L ⊥ A C$ and $D M ⊥ A C$ such that $B L = 8 c m$ and $D M = 7 c m .$ Find the area of quadrilateral $A B C D .$

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Solution

Given: $A C = 24 c m,$ $B L ⊥ A C$ and $D M ⊥ A C$ such that $B L = 8 c m$ and $D M = 7 c m$
Area of quadrilateral $A B C D =$ Area of $△ A D C +$ Area of $△ A C B$
$= \frac{1}{2} \times A C \times D M + \frac{1}{2} \times A C \times B L$
$= \frac{1}{2} \times 24 \times 7 + \frac{1}{2} \times 24 \times 8 c m^{2}$
$= 84 + 96 c m^{2} = 180 c m^{2}$
Hence, the area of the quadrilateral is $180 c m^{2} .$

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In the given figure, ABCD is a quadrilateral in which AC=24cm,BL⊥AC and DM⊥AC such that BL=8 cm and DM=7 cm. Find the area of quadrilateral ABCD.

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In the given figure, $A B C D$ is a quadrilateral in which $A C = 24 c m, B L ⊥ A C$ and $D M ⊥ A C$ such that $B L = 8 c m$ and $D M = 7 c m .$ Find the area of quadrilateral $A B C D .$