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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