# In the given figure, area of ‖ gm ABCD is 80 cm2.Find (i) ar(‖gm ABEF)(ii) ar(∆ABD) and (iii) ar(∆BEF).

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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