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. The bases are right triangles.
An image is shown of a triangular prism. The lengths of the sides of the bases are 4 m, 8 m, and 8.94 m. The height of the triangular prism is 41 m.
(1 point)
Responses
852 m2; 916 m2
852 m 2 ; 916 m 2
859 m2; 891 m2
859 m 2 ; 891 m 2
820 m2; 916 m2
820 m 2 ; 916 m 2
820 m2; 884 m2
820 m 2 ; 884 m 2
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To find the lateral area of the prism, we need to find the perimeter of the base triangle and multiply it by the height of the prism.
The perimeter of the base triangle is the sum of its three sides:
Perimeter = 4 + 8 + 8.94 = 20.94 m
Lateral area = Perimeter * Height = 20.94 * 41 = 857.54 m²
Rounded to the nearest whole number, the lateral area is 858 m².
To find the surface area of the prism, we also need to find the areas of the two triangular bases.
The area of a triangle can be calculated using the formula A = 0.5 * base * height.
For the base triangle with sides of 4 m and 8 m, we can use the Pythagorean theorem to find the height.
Using a = 4, b = 8, and c as the hypotenuse (8.94 m), we have:
c² = a² + b²
(8.94)² = 4² + 8²
c² = 16 + 64
c² = 80
c ≈ 8.944
So, the height of the base triangle is approximately 8.944 m.
Now we can calculate its area:
Area = 0.5 * base * height = 0.5 * 4 * 8.944 = 17.888 m²
Since there are two triangular bases, the total area is 2 * 17.888 = 35.776 m².
Rounded to the nearest whole number, the surface area is 36 m².
Therefore, the correct answer is:
858 m² for the lateral area and 36 m² for the surface area.