AC is one of the diagonals of quadrilateral A | vedclass

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Question

(A) The area of a quadrilateral can be calculated by dividing it into two triangles using a diagonal.$ar(ABCD) = ar(	riangle ABC) + ar(	riangle ADC)

Vedclass · Accepted Answer

$144$

Vedclass · Answer

(A) The area of a quadrilateral can be calculated by dividing it into two triangles using a diagonal.$ar(ABCD) = ar(	riangle ABC) + ar(	riangle ADC)$.The area of a triangle is given by the formula $\frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$.For $	riangle ABC$,the base is $AC = 18 \, cm$ and the height is $BM = 10 \, cm$.$ar(	riangle ABC) = \frac{1}{2} 	imes 18 	imes 10 = 90 \, cm^2$.For $	riangle ADC$,the base is $AC = 18 \, cm$ and the height is $DN = 6 \, cm$.$ar(	riangle ADC) = \frac{1}{2} 	imes 18 	imes 6 = 54 \, cm^2$.Therefore,$ar(ABCD) = 90 + 54 = 144 \, cm^2$.

$AC$ is one of the diagonals of quadrilateral $ABCD$. $BM$ and $DN$ are altitudes on $AC$ from $B$ and $D$ respectively. If $AC = 18 \, cm$,$BM = 10 \, cm$,and $DN = 6 \, cm$,then $ar(ABCD) = \dots \dots \, cm^2$.

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