Evaluating formulas

Heron's formula

Find the area, A units² of the given triangle using the following rule

\(A=\sqrt{\dfrac{(a+b+c)\times(-a+b+c)\times(a-b+c)\times(a+b-c)}{16}}\), where a, b and c are the side lengths of the triangle.

Give your answer correct to one decimal place.

Solution

Let a = 5, b = 7 and c = 8.

A	=\(\sqrt{\dfrac{(a+b+c)\times(-a+b+c)\times(a-b+c)\times(a+b-c)}{16}}\)
	=\(\sqrt{\dfrac{(5+7+8)\times(-5+7+8)\times(5-7+8)\times(5+7-8)}{16}}\)
	=\(\sqrt{\dfrac{20\times10\times6\times4}{16}}\)(Use a calculator.)
	= 17.320...
	= 17.3 cm² correct to one decimal place.

Some simple formulas