Q. 20

# The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.

To Find: Area of the parallelogram

Given: Adjacent sides of parallelogram ABCD: 34 cm and 20 cm

Length of the diagonal = 42 cm

Concept Used:

If sides of a triangle are a, b, and c, then area of a triangle is given by:

Where s = semiperimeter of the triangle

Diagram:

Explanation:

The diagonal of a parallelogram divides the parallelogram into two congruent triangles.

Therefore,

Area of Δ ADC = Area of Δ ABC

Let us calculate area of Δ ABC

s = 48 cm

Area = 4 × 6 × 7 × 2 cm2

Area = 336 cm2

Now, Area of parallelogram ABCD = 2 × 336 cm2

Hence, Area of parallelogram = 672 cm2.

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