Determine the total area of the TWO bases of this triangular prism.
10in, 8in, 12in, 10in, 14in,
(1 point) Responses 48 square inches 48 square inches 96 square inches 96 square inches 188 square inches 188 square inches 448 square inches 448 square inches
The two bases of the triangular prism are triangles with sides of 10in, 8in, and 12in.
To find the area of a triangle using the sides, you can use Heron's formula, which states that the area of a triangle with sides a, b, and c is given by the formula:
Area = √[s(s-a)(s-b)(s-c)]
where s is the semiperimeter of the triangle, calculated by s = (a + b + c) / 2.
Using this formula, we can calculate the area of one triangle base:
s = (10 + 8 + 12) / 2 = 15
Area = √[15(15-10)(15-8)(15-12)]
Area = √[15 * 5 * 7 * 3] = √1575 ≈ 39.68 square inches
Since there are two bases, the total area of both bases is 2 * 39.68 = 79.36 square inches.
So, the total area of the two bases of the triangular prism is approximately 79.36 square inches.