Final answer:
To find the lateral area of a triangular prism, calculate the perimeter of the base triangle and multiply it by the prism's height. The surface area involves adding the lateral area to the area of the two base triangles. Final answers should be rounded to the nearest whole number and consider significant figures.
Step-by-step explanation:
Finding Lateral Area and Surface Area of a Triangular Prism
To find the lateral area of a triangular prism, you need to calculate the perimeter of the base triangle and multiply it by the height of the prism. For the base triangle being a right triangle, add the two legs and the hypotenuse to get the perimeter. The provided dimensions for the right triangle are 8 m (leg1), 41 m (leg2), and 8.94 m (hypotenuse). The perimeter (P) is therefore P = 8 m + 41 m + 8.94 m.
Next, multiply this perimeter by the height (H) of the prism to get the lateral area (LA). The height, based on the question, seems to be unspecified, but if it's one of the given measurements, then LA = P × H.
The surface area of the prism is calculated by adding the lateral area and the areas of the two base triangles. The area of a right triangle is given by (1/2) × base × height, so for one of the base triangles, it's (1/2) × 8 m × 41 m. Since there are two congruent triangles, this area is multiplied by 2 and then added to the lateral area to find the total surface area (SA). SA = LA + 2 × (1/2) × 8 m × 41 m.
Note that we need to round our final answers to the nearest whole number and keep significant figures in mind if the question specifies precision.