Question

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

Answer 1

Answer:

Option B. 770 meter²

Step-by-step 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 = $\frac{1}{2}(Apothem)(perimeter)$

$= \frac{1}{2}(6\sqrt{3})(72)=216\sqrt{3}$

Surface area of triangular sides = $6.\frac{1}{2}(Base)(height)=\frac{6}{2}(12)(11)=(36)(11)=396$

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

Option B. 770 meter² is the answer.

Answer 2

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.

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