Question

Area of parallelogram lmno is 240 sq cm,find area of triangle pmq , parallelogram pmnq

Answer 1

Area of the parallelogram PMNQ = 240 sq. cm

Area of ΔPMQ = 120 sq. cm

Solution:

The image of the question is attached below.

Given parallelogram LMNO = 240 sq. cm

To find the area of the parallelogram PMNQ:

Base of the parallelogram LMNO = MN

Base of the parallelogram PMNQ = MN

LMNO and PMNQ lies between the parallels LM and QN.

Theorem:

Parallelograms between the same and same parallels are equal in area.

Area of the parallelogram PMNQ = Area of the parallelogram LMNO

Area of the parallelogram PMNQ = 240 sq. cm

To find the area of the triangle PMQ:

Base of the ΔPMQ = PQ

One of the base of the parallelogram PMNQ = PQ

Theorem:

If a triangle and a parallelogram are on the same base and between the same parallels, then the area of the triangle is half of the area of the parallelogram.

Area of ΔPMQ = Half of the area of PMNQ

                        = $\frac{1}{2} \times 240$

                        = 120 sq. cm

Area of ΔPMQ = 120 sq. cm

Hence area of the parallelogram PMNQ = 240 sq. cm

Area of ΔPMQ = 120 sq. cm

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