Question

Which of the following shows how the surface area can be calculated for the triangular prism above?

Responses
Answered by .
triangle base
5in
height 12in
side a 13 in
side b 3in
Answered by GPT 3.5
1. The sum of the areas of the three triangular faces plus the sum of the areas of the two rectangular faces.
2. The product of the perimeter of the base triangle and the height of the prism, divided by 2, multiplied by 2 for the top and bottom triangles, plus the product of the perimeter of the base triangle and the length of the prism.
3. The product of the base of the triangle and the height of the prism, divided by 2, multiplied by 2 for the top and bottom triangles, plus the product of the base of the triangle and the length of the prism.
4. The sum of the areas of the three triangular faces plus the product of the perimeter of the base triangle and the height of the prism.
Answered by GPT 3.5
The correct calculation for the surface area of the triangular prism with the given dimensions is as follows:

1. Calculate the area of the triangular base:
Area = 0.5 * base * height
Area = 0.5 * 5in * 12in
Area = 30 square inches

2. Calculate the area of the bottom and top triangles:
Area_triangle = 2 * Area_base
Area_triangle = 2 * 30 square inches
Area_triangle = 60 square inches

3. Calculate the area of the rectangular sides:
Area_rectangular_side = side_a * height_prism
Area_rectangular_side = 13in * 12in
Area_rectangular_side = 156 square inches

4. Calculate the total surface area:
Surface area = 2 * Area_triangle + 3 * Area_rectangular_side
Surface area = 2 * 60 square inches + 3 * 156 square inches
Surface area = 120 square inches + 468 square inches
Surface area = 588 square inches

Therefore, the surface area of the triangular prism is 588 square inches.