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.

Answer :

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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