Answer:
Area = 640 sq. meters
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:
[tex]\begin{gathered} Area_{prism}=Area_{triangle,1}+Area_{triangle,2}+Area_{rectangle,1}+Area_{rectangle,2}+Area_{rectangle,3} \\ Area_{triangle}=\frac{1}{2}\times base\times height \\ Area_{triangle,1}=\frac{1}{2}\times5\times12=30m^2 \\ Area_{triangle,2}=\frac{1}{2}\times5\times12=30m^2 \\ \\ Area_{rectangle}=length\times width \\ Area_{rectangle,1}=20\times12=240m^2 \\ Area_{rectangle,2}=20\times12=240m^2 \\ Area_{rectangle,3}=20\times5=100m^2 \end{gathered}[/tex]
The area of the prism is obtained thus:
[tex]\begin{gathered} Area_{prism}=30+30+240+240+100 \\ Area_{prism}=640m^2 \\ \\ \therefore Area_{prism}=640m^2 \end{gathered}[/tex]
Therefore, the area of the prism is 640 square meters
