Find the area of the parallelogram ABCD in which AB = 14 cm, BC = 10 cm and AC = 16cm. [ Given = 1.73]

According to the question,

In order to find the area of quadrilateral ABCD,

At first,

Let us consider triangle ABC,

Say,

a = 10 cm, b = 16 cm and c = 14 cm

Now,

Semi perimeter of ΔABC, s =

=

=

= 20 cm

Now,

Area of ΔABC =

=

=

= 40√3 cm^{2}

We know that, the diagonal of a parallelogram divides it into two triangles of equal areas.

Hence,

Area of quadrilateral ABCD = Area of ΔABC + Area of ΔACD

= Area of ΔABC × 2

= 40√3 × 2

= 80√3 cm^{2}

= 138.4 cm^{2}

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