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Question
In the figure, ABCD is a parallelogram and APD is an equilateral triangle of side 80cm, Calculate the area of parallelogram ABCD.
Solution
ar(ΔAPD) = `(sqrt(3)"s"^2)/(4)`
ar(ΔAPD) = `(sqrt(3) xx 8^2)/(4)`
ar(ΔAPD) = `(sqrt(3) xx 64)/(4)`
ar(ΔAPD) = `sqrt(3) xx 16 = 16sqrt(3)"cm"^2`
ar(ΔAPD) = `(1)/(2)` x ar(parallelogram ABCD)
(The area of a triangle is half that of a parallelogram on the same base and between the same parallels)
⇒ ar(parallelogram ABCD) = 2 x ar(ΔAPD)
⇒ ar(parallelogram ABCD) = 2 x `16sqrt(3)"cm"^2`
⇒ ar(parallelogram ABCD) = `32sqrt(3)"cm"^2`.
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