Q. 134.5( 2 Votes )
In the given figure, area of ‖ gm ABCD is 80 cm2.
Find (i) ar(‖gm ABEF)
(ii) ar(∆ABD) and (iii) ar(∆BEF).
Answer :
Given: area of ‖ gm ABCD is 80 cm2
We know that any two or parallelogram having the same base and lying between the same parallel lines are equal in area.
∴ ar(||gm ABCD) = ar(||gm ABEF) –1
We also know that when a parallelogram and a triangle lie on same base and between same parallel lines then, area of the triangle is half the area of the parallelogram.
∴ ar(∆ABD) = 1/2 × ar(||gm ABCD) and,
ar(∆BEF) = 1/2 × ar(||gm ABEF)
(i)
ar(||gm ABCD) = ar(||gm ABEF)
∴ ar(||gm ABEF) = 80cm2 (∵ar(||gm ABCD) = 80cm2)
(ii)
ar(∆ABD) = 1/2 × ar(||gm ABCD)
ar(∆ABD) = 1/2 × 80 = 40cm2 (∵ar(||gm ABCD) = 80cm2)
∴ ar(∆ABD) = 40cm2
(iii)
ar(∆BEF) = 1/2 × ar(||gm ABEF)
ar(∆BEF) = 1/2 × 80 = 40cm2 (∵ar(||gm ABEF) = 80cm2)
∴ ar(∆BEF) = 40cm2
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