An image shows a triangular prism with a height of 12, a width of 9 and a length of 9

Question

give the lateral area, the total surface area and the volume

Answer 1

Lateral area of the triangular prism:
To find the lateral area of a triangular prism, we need to find the area of the three rectangular sides.

Area of one rectangular side = height x width = 12 x 9 = 108

Since there are three rectangular sides, the total lateral area = 3 x 108 = 324 square units

Total surface area of the triangular prism:
The total surface area of a triangular prism includes the three rectangular sides and the two triangular ends.

Area of one triangular end = 1/2 x base x height = 1/2 x 9 x 12 = 54

Since there are two triangular ends, the total area = 2 x 54 = 108

Total surface area = lateral area + 2 x area of triangular end
Total surface area = 324 + 108 = 432 square units

Volume of the triangular prism:
The volume of a prism is calculated by multiplying the base area by the height.

Base area = 1/2 x base x height = 1/2 x 9 x 12 = 54

Volume = base area x height = 54 x 9 = 486 cubic units

Therefore, the lateral area of the triangular prism is 324 square units, the total surface area is 432 square units, and the volume is 486 cubic units.