Question

Find the area of the following triangle. Give your answer correct to two decimal places.

8m
9m
3m

Answer 1

Answer: 11.83 square meters

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Step-by-step explanation:

We'll use Heron's Formula.

When given the three sides a,b,c, the area of the triangle is

`A = √(s(s-a)(s-b)(s-c))`

where s = (a+b+c)/2 is the semi-perimeter, aka half the perimeter.

Let's compute the value of s first

s = (a+b+c)/2 = (8+9+3)/2 = 20/2 = 10

Then we can say,

`A = √(s(s-a)(s-b)(s-c))\\\\A = √(10(10-8)(10-9)(10-3))\\\\A = √(140)\\\\A \approx 11.8321595661992\\\\A \approx 11.83\\\\`

The triangle has area of roughly 11.83 square meters.