Question

use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.

Answer 1

`671m^(2);725m^(2)`

Explanation:

Answer 2

Second Option

671 m²; 725 m²

Explanation:

The lateral area of a triangular prism is:

`A_L = Ph`

Where P is the perimeter of the triangular base and h is the height of the prism.

In this case, the perimeter of the triangular base is:

`P = 9 + 6+ 10.82\\\\P = 25.82\ m`

Then the height is 26 m

Then the lateral area of the prism is:

`A_L = 25.82 * (26)\\\\A_L = 671\ m ^ 2`

Therefore the surface area of the triangular prism is:

`A = 2A_B + A_L`

Where
`A_B` is the area of the base.

`A_B = (bh)/(2)`

Where b is the base of the triangle and h is the height

In this case:

`b = 9\ m\\\\h = 6\ m\\\\A_B = (9 * 6)/(2)\\\\A_B = 27\ m ^ 2`

Finally

`A = 2 * 27 + 671\\\\A = 54 + 671\\\\A = 725\ m ^ 2`

The answer is 671 m² and 725 m²