Question

Find the area of a quadrilateral ABCD is which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

Answer 1

The quadrilateral ABCD having sides AB, BC, CD, DA and diagonal AC=5 cm is given, where AC divides quadrilateralABCD into two triangles ΔABC and ΔADC. We will find the area of the two triangles separately and them to find the area of quadrilateral ABCD.

In triangle ΔABC, observe that,

So the triangle ΔABC is right angled triangle.

Area of right angled triangle ΔABC, is given by

In ΔACD all the sides are known, so just use Heron’s formula to find out Area of triangle ΔACD,

$$\begin{gathered} s=\frac{AD+DC+AC}{2} \\ =\frac{5+4+5}{2} \\ =7\mathrm{cm} \end{gathered}$$

The area of the ΔACD is:

Area of quadrilateral ABCD will be,

Area = Area of triangle ABC + Area of triangle ADC