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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