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.
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
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)