Question

What is the surface area of triangular pyramid?​

Answer 1

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

$\sf A=\dfrac{1}{2}bh$

where:

• b = base
• h = height

From inspection of the diagram:

• Base triangle:  b = 10 in,  h = 8.7 in
• Side triangles:  b = 20 in,  h = 12 in

$\begin{aligned}\implies \textsf{Area of the base triangle} & = \sf \dfrac{1}{2} \cdot 10 \cdot 8.7\\& = \sf 5 \cdot 8.7\\& =\sf 43.5\:in^2\end{aligned}$

$\begin{aligned}\implies \textsf{Area of a side triangle} & = \sf \dfrac{1}{2} \cdot 10 \cdot 12\\& = \sf 5 \cdot 12\\& =\sf 60\:in^2\end{aligned}$

$\begin{aligned}\implies \textsf{S.A. of the triangular pyramid} & = \textsf{base triangle}+\textsf{3 side triangles}\\& = \sf 43.5 + 3(60)\\& = \sf 43.5 + 180\\& = \sf 223.5\:in^2\end{aligned}$

Therefore, the surface area of the given triangular pyramid is 223.5 in².