Find the area of a right triangle has 3 sides with the lengths of 29.1, 20.4 and 14.6
Answer Choices: (Pick 1)
297.84 in2 297.84 in2 212.43 in2 212.43 in2 148.92 in2 148.92 in2 424.86 in2
The area of a triangle can be calculated using the formula A = 0.5 * base * height.
First, we need to find the height of the triangle. We can use the formula for the area of a triangle in terms of its sides and the semiperimeter (s) of the triangle, which is given by s = (a + b + c) / 2, where a, b, and c are the lengths of the sides.
In this case, the sides are a = 29.1, b = 20.4, and c = 14.6. The semiperimeter is s = (29.1 + 20.4 + 14.6) / 2 = 32.05.
Now, we can use Heron's formula to find the height:
Area = sqrt[s(s - a)(s - b)(s - c)]
Area = sqrt[32.05(32.05 - 29.1)(32.05 - 20.4)(32.05 - 14.6)]
Area = sqrt[32.05(2.95)(11.65)(17.45)]
Area = sqrt(1994.16)
Area ≈ 44.67
Now that we've found the height, we can calculate the area of the triangle:
Area = 0.5 * base * height
Area = 0.5 * 20.4 * 44.67
Area = 444.24
Therefore, the area of the right triangle is approximately 444.24 in². The closest answer choice is 424.86 in².