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
To find the lateral area of the prism, you need to find the area of all the sides except the bases. Since the bases are right triangles, you can find the area of each triangular side using the formula 1/2 * base * height.
For the first triangular side, the base is 8m and the height is 41m, so the area is 1/2 * 8m * 41m = 164m².
For the second triangular side, the base is 4m and the height is 41m, so the area is 1/2 * 4m * 41m = 82m².
Since there are two triangular sides, the total lateral area is 164m² + 82m² = 246m².
To find the surface area, you need to add the lateral area to the area of the bases. The area of each base can be found using the formula 1/2 * base * height.
For the first base, the base is 8m and the height is 41m, so the area is 1/2 * 8m * 41m = 164m².
For the second base, the base is 4m and the height is 41m, so the area is 1/2 * 4m * 41m = 82m².
Since there are two bases, the total area of the bases is 164m² + 82m² = 246m².
Adding the lateral area of 246m² to the area of the bases of 246m² gives a total surface area of 246m² + 246m² = 492m².
Rounding to the nearest whole number, the lateral area is approximately 246m² and the surface area is approximately 492m².
Therefore, the correct answer is:
246 m²; 492 m².