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

Answer:

Second Option

671 m²; 725 m²

Step-by-step 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.

$A_B = \frac{bh}{2}$

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

In this case:

$b = 9\ m\\\\h = 6\ m\\\\A_B = \frac{9 * 6}{2}\\\\A_B = 27\ m ^ 2$

Finally

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

The answer is 671 m²  and  725 m²