Question

Finding the surface area of a prism #5 and #6

Answer 1

Area = 640 sq. meters

Step-by-step explanation:

5.

We are given the figure of a prism and we are to obtain its surface area

The prism has 5 faces: 2 triangular shaped faces of equal dimensions, 3 rectangular faces of different dimensions (2 out of these 3 have the same dimension while the third has a different dimension)

For the triangular-shaped face(s), its/their dimension is:

Height = 12 inches

Base = 5 inches

For the rectangular-shaped faces, their dimensions are:

Rectangle 1 & 2: Length = 20 inches, Width = 12 inches

Rectangle 3: Length = 20 inches, Width = 5 inches

The surface area of the prism is obtained by the sum of all the areas of the 5 faces itemized above. This is shown below:

`\begin{gathered} Area_(prism)=Area_(triangle,1)+Area_(triangle,2)+Area_(rectangle,1)+Area_(rectangle,2)+Area_(rectangle,3) \\ Area_(triangle)=(1)/(2)* base* height \\ Area_(triangle,1)=(1)/(2)*5*12=30m^2 \\ Area_(triangle,2)=(1)/(2)*5*12=30m^2 \\ \\ Area_(rectangle)=length* width \\ Area_(rectangle,1)=20*12=240m^2 \\ Area_(rectangle,2)=20*12=240m^2 \\ Area_(rectangle,3)=20*5=100m^2 \end{gathered}`

The area of the prism is obtained thus:

`\begin{gathered} Area_(prism)=30+30+240+240+100 \\ Area_(prism)=640m^2 \\ \\ \therefore Area_(prism)=640m^2 \end{gathered}`

Therefore, the area of the prism is 640 square meters