Question

ABCD is a parallelogram &is the mid-point of AB. If ar(AXCD)=24cmsquare. then find ar(ABC).

Answer 1

We know that the area of a triangle is half of that of a parallelogram if they are on the same base and between the same parallels.

In case triangle XCB, base is half. Therefore, area of triangle XCB

= 1/2 x 1/2 ar(ABC)

=1/4 ar(ABC)

Now ar(AXCD) = ar(ABCD) - ar(XCB)

= 1 - 1/4

= 3/4

As area of AXCD is 3/4ar(ABCD), area of ABCD

= 24 x 4/3

= 32cm²

We know that a diagonal divides a parallelogram into two triangles of equal area.

Thus area of ABC = 1/2 ar(ABCD)

or, ar(ABC) = 1/2 x 32

or, ar(ABC) = 16cm²