Question

What is the surface area of the triangular prism? its sides are 9,8,10, and 6.

Answer 1

To calculate the surface area of a triangular prism, we need to find the areas of the three rectangular faces and two triangular faces.

Given that the sides of the triangular prism are 9, 8, 10, and 6, we can determine the following:
- The base of one of the triangles has sides of length 9, 8, and 10. This can be solved using Heron's formula for finding the area of a triangle given its side lengths.

The semiperimeter of the triangle is (9+8+10)/2 = 13.5
Area of the triangle = √(13.5*4.5*5.5*3.5) = √(91.125) ≈ 9.55

- The other base triangle has a base of 6 and a height of 8.
Area of the triangle = (1/2)*base*height = (1/2)*6*8 = 24 units^2

- The three rectangular faces have areas equal to the product of their respective sides:
9*8 = 72 units^2
9*10 = 90 units^2
8*10 = 80 units^2

Adding everything up, we get the total surface area of the triangular prism:
Total surface area = 2* triangle area + 3* rectangle area
Total surface area = 2*(9.55 + 24) + 3*(72 + 90 + 80)
Total surface area ≈ 279.1 units^2

Therefore, the surface area of the triangular prism is approximately 279.1 units^2.