Question

What is the surface area of the triangular prism?

The area of the bottom face is ___ m2

The area of one of the rectangular side faces is ___ m2

The area of one of the triangular faces is ___ m2

The surface area of the prism is ___ m2

Answer 1

The surface area of the prism is
`A_(prism)=204 \:m^2`.

Explanation:

Area is the space that is contained in a two-dimensional figure.

Surface area is the total area of all of the sides and faces of a three-dimensional figure.

To find the surface area, the area of each face is calculated and then add these areas together.

• To find the area of a rectangle, multiply the length by the width
  `A=l\cdot w`.

From the graph the length of the rectangle is 10 m and the width is 8 m. Therefore, the area of the bottom face is

`A_(Bottom)=8\cdot 10=80 \:m^2`

From the graph the length of the rectangle is 10 m and the width is 5 m. Therefore, the area of one of the rectangular side faces is

`A_(side)=5\cdot 10=50 \:m^2`

• To find the area of a triangle use the following formula
  `A=(1)/(2)bh` where b is the base and h is the height.

From the graph the base of the triangle is 8 m and the height is 3 m. Therefore, the area of one of the triangular faces is

`A_(triangle)=(1)/(2) 8\cdot 3=12 \:m^2`

• The surface area of the prism is the sum of the area of the bottom face, the area of the two rectangular side faces, and the area of the two triangular faces

`A_(prism)=A_(bottom)+2A_(side)+2A_(triangle)=80+2\cdot50+2\cdot12=204 \:m^2`