Question

if sides of a triangle are 15m,11m and 6m then find the area using heros formula

Answer 1

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Answer 2

The area of the triangle is 20√2.

Given,

The length of the sides of the triangle = 15m, 11m, and 6m

To Find,

The area of the triangle using Heron's formula

Solution,

We can find the area of a triangle, given its three sides, using the Heron's formula

The area of a triangle given its sides a, b, and c is given by:

$Area = \sqrt{s(s-a)(s-b)(s-c)}$

where s is the semiperimeter of the triangle, which is calculated as follows:

$s = \frac{a+b+c}{2}$

In the given triangle,

$s = \frac{15+11+6}{2}\\\\s = \frac{32}{2}\\\\s = 16$

Therefore, the area is given by:

$Area = \sqrt{16 \times (16-15) \times (16-11) \times (16-6)}\\Area = \sqrt{16 \times 1 \times 5 \times 10}\\Area = \sqrt{800}\\Area = 20\sqrt{2}$

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