Question

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

Answer 1

if you look at the pyramid, the pyramid is really just a hexagon with 6 triangles stacked up to each other at the edges, with the hexagon at the bottom.

now, the perpendicular distance from the center of the hexagon to a side, namely the apothem, is 6√3, and each side is 12 units long, since there are 6 of them that'd be 72 for all, namely the perimeter.

each of the triangular faces have a base of 12 and an altitude or height of 11, recall that area of a triangle is (1/2)bh, and area of a regular polygon is (1/2)(apothem)(perimeter).

so if we just get the area of the hexagon at the bottom, and the triangles, sum them up, that's the surface area of the pyramid.


`\bf \stackrel{\textit{area of the hexagon}}{\left[\cfrac{1}{2}(6√(3))(72) \right]}~~~~+~~~~\stackrel{\textit{area of the 6 triangles}}{6\left[\cfrac{1}{2}(12)(11) \right]}`

Answer 2

Option B. 770 meter²

Explanation:

We have to find the surface area of the regular pyramid with a hexagonal base.

Surface area of pyramid = area of triangles at the lateral sides + area of base (Hexagon)

Surface area of hexagonal base =
`(1)/(2)(Apothem)(perimeter)`

`= (1)/(2)(6√(3))(72)=216√(3)`

Surface area of triangular sides =
`6.(1)/(2)(Base)(height)=(6)/(2)(12)(11)=(36)(11)=396`

Now total surface area = 216√3 + 396 = 374 + 396 = 770 meter²

Option B. 770 meter² is the answer.