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.

Answer: 123.32 cm2

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.

Answer: 34º

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)