Q. 134.5( 2 Votes )

# In the given figure, area of ‖ gm ABCD is 80 cm^{2}.

Find (i) ar(‖gm ABEF)

(ii) ar(∆ABD) and (iii) ar(∆BEF).

Answer :

Given: area of ‖ gm ABCD is 80 cm^{2}

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) = 80cm^{2} (∵ar(||gm ABCD) = 80cm^{2})

(ii)

ar(∆ABD) = 1/2 × ar(||gm ABCD)

ar(∆ABD) = 1/2 × 80 = 40cm^{2} (∵ar(||gm ABCD) = 80cm^{2})

∴ ar(∆ABD) = 40cm^{2}

(iii)

ar(∆BEF) = 1/2 × ar(||gm ABEF)

ar(∆BEF) = 1/2 × 80 = 40cm^{2} (∵ar(||gm ABEF) = 80cm^{2})

∴ ar(∆BEF) = 40cm^{2}

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