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what is the surface area of triangular pyramid?​

What Is The Surface Area Of Triangular Pyramid class=

Sagot :

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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:

  • 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

[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.

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