Area of Any Triangle

# Area of Any Triangle

GCSE(H),

The area of a right angled triangle is A = frac(1)(2)bh, where b is the base length and h is the vertical height.

For the triangle ABC, the area of the triangle is frac(1)(2)bh.

Using the trigonometrical ratios, the vertical height is h = a x sin C.

Substituting into the formula for h in the area of a right angled triangle:

A = frac(1)(2)b x a x sin C

= frac(1)(2)ab sin C

## Examples

1. What is the area of the triangle, below? Give your answer correct to 2 decimal places.

Area of any triangle = frac(1)(2)ab sin C

A = frac(1)(2) xx 14 xx 19 xx sin 68

A = 123.3155, or 123.32 (2dp)

2. The area of the triangle below is 100 cm2. What is the size of the angle x? Give your answer correct to the nearest degree.

Area of any triangle = frac(1)(2)ab sin C
100 = frac(1)(2) xx 18 xx 20 xx sin *x*
100 = 180 sin x
0.5556 = sin x
sin^-1^ 0.5556 = x
x = 33.749, or 34º (nearest degree)