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
If sides of a triangle are a, b, and c, then area of a triangle is given by:
Where s = semiperimeter of the triangle
The diagonal of a parallelogram divides the parallelogram into two congruent triangles.
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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