Q2. Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.
From the figure:
We have joined the AC to form two triangles so that the calculation of the area will be easy.
The area of the triangle ABC can be calculated by Heron's formula:
So, the semi-perimeter, where
Heron's Formula for calculating the area:
And the sides of the triangle ACD are
So, the semi-perimeter of the triangle:
Therefore, the area will be given by, Heron's formula
Then, the total area of the quadrilateral will be:
Hence, the area of the quadrilateral ABCD is
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