Question

4. 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. top(8.94m) side(41m) bottom left corner(4m) bottom(8m). ~852 m2; 916 m2 ~859 m2; 891 m2 ~820 m2; 916 m2 ~820 m2; 884 m2 5. Find the surface area of the cylinder to the nearest whole number. The figure is not drawn to scale. 12in , 17in ~ 905 in2 ~ 1,282 in2 ~ 2,187 in2 ~ 7,691 in2

Answer 1

4.) The lateral area of a figure is the area of the figure with the exception of the bases.
Given a prism with right triangle bases, the lateral area of the prism is the sum of the areas of the rectangles making up the prism.
This is given by
Lateral area = (8.94)(41) + (4)(41) + (8)(41) = 366.54 + 164 + 328 = 858.54 ≈ 859 m^2

The surface area is the sum of the bases plus the lateral area. The area of a rectangle is given by half base times height.
Surface area = 1/2 x 8 x 4 + 1/2 x 8 x 4 + 859 = 16 + 16 + 859 = 891 m^2

5.) The surface area of a cylinder is given by pi r^2h where r is the radius = 12 inches and h is the height = 17 inches.
Surface area = π x (12)^2 x 17 = 2,448π = 7,690.62 in^2 ≈ 7,691 in^2