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.

Question

Height: 2 m Length: 9 m Width: 47 m Slope: 9.23 m

A. 951 m^2 ; 958 m^2
B. 951 m^2 ; 969 m^2
C. 940 m^2 ; 958 m^2
D. 940 m^2 ; 969 m^2

Answer 1

To find the lateral area, we need to find the perimeter of the base and multiply it by the height. The base is a trapezoid with bases of 9 m and 47 m, and a height of 9.23 m. Using the formula for the perimeter of a trapezoid, P = b1 + b2 + 2s, where s is the slant height, we get:

P = 9 + 47 + 2(9.23) = 74.46 m

So the lateral area is:

Lateral area = Ph = 74.46 x 2 = 148.92 m^2

To find the surface area, we add the area of the two bases to the lateral area. The area of each base is simply the length times the width, so:

Area of each base = 9 x 47 = 423 m^2

So the surface area is:

Surface area = 2(423) + 148.92 = 994.92 m^2

Rounding to the nearest whole number, we get:

Option B: 951 m^2 (lateral area) and 969 m^2 (surface area)