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.
7.28
29 m
2 m
7 m
(1 point)
O 472 m7: 486 m₴
• 443 m?: 486 m₴
• 472 m'; 479 m₴
• 443 m2: 500 m₴
To find the lateral area of a prism, you need to find the perimeter of the base (Pb) and multiply it by the height (h).
The base of the prism is a rectangle, so the perimeter is calculated as follows:
Pb = 2(length + width)
Given:
Length = 2 m
Width = 7 m
Pb = 2(2 + 7) = 2(9) = 18 m
Now you can find the lateral area:
Lateral Area = Pb * h = 18 m * 29 m = 522 m² (rounded to the nearest whole number)
To find the surface area of the prism, you need to find the area of the two bases (Ab) and add them to the lateral area.
The area of a rectangle is given by:
Ab = length * width = 2 m * 7 m = 14 m²
Now you can find the surface area:
Surface Area = 2(Ab) + Lateral Area = 2(14 m²) + 522 m² = 28 m² + 522 m² = 550 m² (rounded to the nearest whole number)
Therefore, the correct answer is:
• 472 m²; 486 m²