Each side of a triangular pyramid is of length 8 m, the height of the base triangle is 10 m, and the slant height is 15 m. Find its total surface area.

The given values are

l = 8 m , h = 10 m and h = 15 m

To find the total surface area of a triangular pyramid formula is

A_tri-pyramid ​= \$1/2 ​times\$ Perimeter of Base \$times\$ Slant Height + Base Area

Now find the perimeter of the base then after simpler

⇒ P = 3a

⇒ \$P = 3 times 8\$

⇒ P = 24 m

Now find the base area then after simpler

\$"A_base"​ = 1/2 times​ "Base Length" times "Height"\$

Now plug the value in the base area formula then after simpler

\$"A_base" = 1/2 times 8 times 10\$

\$"A_base" = 40 m^2\$

Now plug the values in the total surface area of a triangular pyramid formula

\$"A_tri-pyramid" ​= 1/2 ​times 24 times 15 + 40\$

\$"A_tri-pyramid" = 180 + 40 \$

\$"A_tri-pyramid" = 220 m^2 \$

Therefore, the total surface area of the triangular pyramid is \$220 m^2\$

Can you summarize what you’ve understood in the above steps?

This is incorrect because it only represents the lateral area and does not include the base area in the calculation

180 sq.m

This is correct as it represents the total surface area of the triangular pyramid

220 sq.m

This is not correct because it represents only the area of the triangular base, not the total surface area of the pyramid

40 sq.m

This is incorrect because it is a small value for the surface area of a triangular pyramid

24 sq.m

Option

B

Can you summarize what you’ve understood in the above steps?