The composite figure shown is made up of 2 triangular prisms and one rectangular prism. If the area of each triangle base of the triangular prisms has an area of 24 m2, what is the total surface area of the composite figure? 120 m2 160 m2 760 m2 1,152 m2

A rectangular prism and 2 triangular prisms. The rectangular prism has a length of 20 meters, width of 6 meters, and height of 8 meters. The triangular prisms each have 2 triangular sides with a base of 6 meters and height of 8 meters. The rectangular sides are 20 meters by 6 meters, 20 meters by 10 meters, and 20 meters by 8 meters.

The composite figure shown is made up of 2 triangular prisms and one rectangular prism. If the area of each triangle base of the triangular prisms has an area of 24 m2, what is the total surface area of the composite figure?

How to determine the surface area?

The given parameters are:

Rectangular prism :

Length = 20 meters; Width = 6 meters; Height = 8 meters

Triangular prism :

Triangular sides (2): Base = 6 meters; Height = 8 meters
Rectangular sides: 20 meters by 6 meters, 20 meters by 10 meters, and 20 meters by 8 meters.
Base Area = 24 square meters:

The area of the rectangular prism is:

Area = 2 * (Length * Width + Length * Height + Width * Height)

So, we have:

Area = 2 * (20 * 6 + 20 * 8 + 6 * 8)

Area = 656

The area of the triangular prism is:

Area = 2 * Base Area + Areas of Rectangular sides

So, we have:

Area = 2 * 24 + (20 * 6 + 20 * 10 + 20 * 8)

Area = 528

The common area between the prisms is:

Common area = 8 * 4

Common area = 32

Subtract the common area from the sum of the areas of the triangular prism and the rectangular prism to get the area of the composite figure

Composite figure = 656 + 528 - 32

Evaluate the sum

Composite figure = 1152

Hence, the area of the composite figure is 1152 square meters