Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number. The figure is not drawn to scale. The bases are right triangles.
An image is shown of a triangular prism. The lengths of the sides of the bases are 4 m, 8 m, and 8.94 m. The height of the triangular prism is 41 m.
(1 point)
To find the lateral area of a prism, you need to find the perimeter of the base and then multiply it by the height of the prism.
Perimeter of base = 4 + 8 + 8.94 = 20.94 m
Lateral area = Perimeter of base * height = 20.94 m * 41 m = 859.14 m²
To find the surface area of a prism, you need to find the sum of the lateral area and the areas of the two bases.
Area of one base (triangle) = 1/2 * base * height = 1/2 * 8 m * 4 m = 16 m²
Total surface area = Lateral area + 2 * base area = 859.14 m² + 2 * 16 m² = 891.14 m²
Therefore, the lateral area of the prism is 859 m² and the surface area is 891 m².