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.
H = 4
W = 8
L = 41
hypotenuse = 8.94
To find the lateral area of a triangular prism, you first need to calculate the area of the three rectangular sides and then add those areas together.
1. Calculate the area of one rectangular side:
Area = H * L
Area = 4 * 41
Area = 164
2. Calculate the total lateral area by multiplying by 3 (since there are three rectangular sides):
Lateral Area = 3 * Area
Lateral Area = 3 * 164
Lateral Area = 492
To find the total surface area of the prism, you need to add the lateral area to the area of the two triangular bases.
1. Calculate the area of one triangular base:
Area = 1/2 * H * W
Area = 1/2 * 4 * 8
Area = 16
2. Calculate the total surface area by adding the lateral area and the two triangular base areas:
Surface Area = Lateral Area + 2 * Area
Surface Area = 492 + 2 * 16
Surface Area = 492 + 32
Surface Area = 524
Therefore, the lateral area of the prism is 492 and the surface area is 524.