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.

Question

8.94 m
41 m
4 m
8 m
(1 point)
•. 852 m: 916 m?
•: 859 m2: 891 m₴
•: 820 m2: 916 m?
820 m₽: 884 m2

Answer 1

To find the lateral area of a prism, we need to find the perimeter of the bases and multiply it by the height.

Perimeter of the base = sum of all sides
= 8 m + 8 m + 41 m
= 57 m

Lateral area = Perimeter of the base * height
= 57 m * 8.94 m
≈ 511.58 m²
≈ 512 m² (rounded to the nearest whole number)

To find the surface area of a prism, we need to find the lateral area and add the area of the two bases.

Area of the base = 1/2 * base * height
= 1/2 * 8 m * 41 m
= 164 m²

Surface area = Lateral area + 2 * Area of the base
= 512 m² + 2 * 164 m²
= 840 m²

So, the correct answer is:
- Lateral area: 512 m²
- Surface area: 840 m²