Question

Find the surface area of the regular pyramid shown to the nearest whole number. The figure is not drawn to scale.

A. 351 m^2
B. 415 m^2
C. 542 m^2
D. 790 m^2

Answer 1

`\text{The surface area is }351 m^2`

Explanation:

Given a regular pyramid we have to find the surface area of regular pyramid.

Side of base(regular hexagon)=13 m

Slant height=l=9 m

`\text{Perimeter of regular hexagon=}13* 6=78m`

`\text{Surface area=}(1)/(2)* \text{perimeter of base}* \text{slant height}`

`=(1)/(2)* 78* 9=351 m^2`

Option A is correct.

Answer 2

Option D. 790 m²

Explanation:

Surface area of the regular pyramid = surface area of hexagonal base + 6×Surface area of slant triangular side

Surface area of the hexagonal base =
`(3√(3) )/(2)(side)^(2)`

=
`(3√(3) )/(2)(13)^(2)=((3)(169)√(3))/(2)`

= 439 m²

Surface area of slant side =
`(1)/(2)(Base)(Height)=(1)/(2)(13)(9)`

= 58.5 m²

Surface area of the pyramid = 439 + 6×58.5 = 439 + 351 = 790 m²

Option D. 790 m² is the answer.