Question

In a quadrilateral ABCD, AB = 28 cm, BC = 26 cm, CD = 50 cm, DA = 40 cm and diagonal AC = 30 cm. Find the area of the quadrilateral.

Answer 1

ABCD is a quadrilateral which can be divided into two triangles.

$△ABC\text{and}△ADC$

Using the Heron’s formula

Area of a triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

Where $s=\frac{(a+b+c)}{2}$

For $△$ ABC

$s=\frac{28+26+30}{2}=42$

Area of $△$ ABC
= $\sqrt{42(42-28)(42-26)(42-30)}$

=$\sqrt{42\times 14\times 16\times 12}$

=$\sqrt{112896}$

=336 cm${}^2$

For $△$ ADC

$s=\frac{30+40+50}{2}=60$

Area of $△$ ADC

=$\sqrt{60(60-30)(60-40)(60-50)}$

=$\sqrt{60\times 30\times 20\times 10}$

=$\sqrt{360000}$

=600 cm${}^2$

Area of quadrilateral ABCD = (600 + 336) cm${}^2$

= 936 cm${}^2$