ABCD is a parallelogram. If operatorname{ar}( | vedclass

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(A) diagonal of a parallelogram divides it into two triangles of equal area.In parallelogram $ABCD$,the diagonal $AC$ divides the parallelogram into t

Vedclass · Accepted Answer

$84$

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(A) diagonal of a parallelogram divides it into two triangles of equal area.In parallelogram $ABCD$,the diagonal $AC$ divides the parallelogram into two triangles,$	riangle ABC$ and $	riangle ADC$.Therefore,$\operatorname{ar}(ABC) = \operatorname{ar}(ADC)$.The area of the parallelogram is the sum of the areas of these two triangles:$\operatorname{ar}(ABCD) = \operatorname{ar}(ABC) + \operatorname{ar}(ADC)$.Since $\operatorname{ar}(ABC) = 42 \, 	ext{cm}^2$,then $\operatorname{ar}(ADC) = 42 \, 	ext{cm}^2$.Thus,$\operatorname{ar}(ABCD) = 42 \, 	ext{cm}^2 + 42 \, 	ext{cm}^2 = 84 \, 	ext{cm}^2$.

$ABCD$ is a parallelogram. If $\operatorname{ar}(ABC) = 42 \, \text{cm}^2$,then find $\operatorname{ar}(ABCD)$ in $\text{cm}^2$.

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