# Calculate the area of a circle inscribed in a triangle with sides 18, 24, 30.

July 29, 2021 | education

| We find out what value will be equal to half of the perimeter of this triangle:

(30 + 24 + 18): 2 = 36.

Now we will find out what size its area will equal, for which we will use the Heron’s formula known from the school course:

√ (36 * (36 – 30) * (36 – 24) * (36 – 18)) = √ (36 * 6 * 12 * 18) = 6 * 6 * 2 * 3 = 216.

Now we can calculate the radius of the circle that is inscribed in this triangle:

216: 36 = 6.

Knowing the radius, we can calculate its area:

3.14 * 6 ^ 2 = 113.04.

Answer: 113.04.

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