Answer:
223.5 in²
Step-by-step explanation:
The surface area of a triangular pyramid comprises:
- Area of the base triangle.
- Area of 3 congruent side triangles.
Area of a triangle
[tex]\sf A=\dfrac{1}{2}bh[/tex]
where:
From inspection of the diagram:
- Base triangle: b = 10 in, h = 8.7 in
- Side triangles: b = 20 in, h = 12 in
[tex]\begin{aligned}\implies \textsf{Area of the base triangle} & = \sf \dfrac{1}{2} \cdot 10 \cdot 8.7\\& = \sf 5 \cdot 8.7\\& =\sf 43.5\:in^2\end{aligned}[/tex]
[tex]\begin{aligned}\implies \textsf{Area of a side triangle} & = \sf \dfrac{1}{2} \cdot 10 \cdot 12\\& = \sf 5 \cdot 12\\& =\sf 60\:in^2\end{aligned}[/tex]
[tex]\begin{aligned}\implies \textsf{S.A. of the triangular pyramid} & = \textsf{base triangle}+\textsf{3 side triangles}\\& = \sf 43.5 + 3(60)\\& = \sf 43.5 + 180\\& = \sf 223.5\:in^2\end{aligned}[/tex]
Therefore, the surface area of the given triangular pyramid is 223.5 in².
