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

Answer:

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

Step-by-step 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

$\text{Perimeter of regular hexagon=}13\times 6=78m$

$\text{Surface area=}\frac{1}{2}\times \text{perimeter of base}\times \text{slant height}$

$=\frac{1}{2}\times 78\times 9=351 m^2$

Option A is correct.

Answer 2

Answer:

Option D. 790 m²

Step-by-step 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 = $\frac{3\sqrt{3} }{2}(side)^{2}$

= $\frac{3\sqrt{3} }{2}(13)^{2}=\frac{(3)(169)\sqrt{3}}{2}$

= 439 m²

Surface area of slant side = $\frac{1}{2}(Base)(Height)=\frac{1}{2}(13)(9)$

= 58.5 m²

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

Option D. 790 m² is the answer.