Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number. Use the large 12 x 7 m rectangles on the top and bottom as the bases.
A rectangular prism is shown. The height is 2 meters, the width is 7 meters, and the length is 12 meters.
(1 point)
Responses
76 m2; 244 m2
76 m 2 ; 244 m 2
76 m2; 160 m2
76 m 2 ; 160 m 2
216 m2; 160 m2
216 m 2 ; 160 m 2
216 m2; 244 m2
To find the lateral area of the prism, we need to find the sum of the areas of the four vertical faces.
The height of the prism is 2 meters and the width is 7 meters. Since two of the faces have dimensions of 2 meters by 7 meters, their combined area is 2*7 + 2*7 = 28 square meters.
The length of the prism is 12 meters. Since the other two faces have dimensions of 2 meters by 12 meters, their combined area is 2*12 + 2*12 = 48 square meters.
Adding the areas of the four vertical faces together, we get 28 + 48 = 76 square meters.
Therefore, the lateral area of the prism is 76 m^2.
To find the surface area of the prism, we need to add the areas of the two bases to the lateral area.
The base of the prism is a rectangle with dimensions of 12 meters by 7 meters. The area of one base is 12*7 = 84 square meters. Since there are two bases, their combined area is 2*84 = 168 square meters.
Adding the lateral area of 76 square meters to the base areas of 168 square meters, we get 76 + 168 = 244 square meters.
Therefore, the surface area of the prism is 244 m^2.