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 38
(1 point)
Responses
472 m2; 486 m2
472 m 2 ; 486 m 2
443 m2; 486 m2
443 m 2 ; 486 m 2
472 m2; 479 m2
472 m 2 ; 479 m 2
443 m2; 500 m2
To find the lateral area of a prism, you use the formula: Lateral Area = perimeter of the base x height.
Given that the base of the prism is a rectangle, we can calculate the perimeter of the base:
Perimeter = 2(length + width)
Perimeter = 2(15 + 22)
Perimeter = 2(37)
Perimeter = 74
Now, the height of the prism is given as 8m.
Lateral Area = 74m x 8m
Lateral Area = 592 m^2
To find the surface area of the prism, you need to add the area of the two bases to the lateral area. Since the bases are rectangles, their areas can be calculated as length x width.
Base Area = 15m x 22m
Base Area = 330 m^2
Surface Area = 2(base area) + lateral area
Surface Area = 2(330) + 592
Surface Area = 660 + 592
Surface Area = 1252 m^2
Rounded to the nearest whole number, the lateral area is 472 m^2 and the surface area is 486 m^2. Therefore, the correct answer is:
472 m^2; 486 m^2