Given:
Required:
To find the total surface area of the prism.
Explanation:
The total surface area of the prism is given by the formula:
[tex]A=2\times base\text{ area+Area of the rectangle}[/tex]
Area of the base triangle
[tex]\begin{gathered} =\frac{1}{2}\times base\times height \\ =\frac{1}{2}\times6\times8 \\ =\frac{48}{2} \\ =24\text{ cm}^2 \end{gathered}[/tex]
To find the width of the rectangle we will use the Pythagoras theorem.
[tex]\begin{gathered} width=\sqrt{(8)^2+(6)^2} \\ width=\sqrt{64+36} \\ width=\sqrt{100} \\ width=10\text{ cm} \end{gathered}[/tex]
Area of the rectangle
[tex]\begin{gathered} =length\times breadth \\ =12\times10 \\ =120cm^2 \end{gathered}[/tex]
Thus the area of the prism
[tex]\begin{gathered} =2\times24+120 \\ =48+120 \\ =168\text{ cm}^2 \end{gathered}[/tex]
Final Answer:
