Question

In a ΔABC, AB = 15 cm, BC = 13 cm and AC = 14 cm. Find the area of ΔABC and hence its altitude on AC.

Answer 1

Whenever we are given the measurement of all sides of a triangle, we basically look for Heron’s formula to find out the area of the triangle.

If we denote area of the triangle by ‘Area’, then the area of a triangle having sides a, b, c and s as semi-perimeter is given by;

Where,
We are given:

AB = 15 cm, BC = 13 cm, AC = 14 cm

Here we will calculate s,

So the area of the triangle is:

Now draw the altitude from point B on AC which intersects it at point D.BD is the required altitude. So if you draw the figure, you will see,

Here . So,