Find the lateral area and the surface area of the regular hexagonal pyramid.

question 8 options:

lateral area = 385.1 cm2; surface area = 805 cm2

lateral area = 231.6 cm2; surface area = 441 cm2

lateral area = 210 cm2; surface area = 325.5 cm2

lateral area = 21.8 cm2; surface area = 231.2 cm2

Part 1) The lateral area is

Part 2) The surface area is

so

lateral area = 210 cm2; surface area = 325.5 cm2

Step-by-step explanation:

Part 1) Find the lateral area of the regular hexagonal pyramid

The lateral area is equal to the area of its six triangular faces

so

we have

substitute

Part 2) Find the surface area of the regular hexagonal pyramid

The surface area is equal to the lateral area plus the area of the hexagonal base

so

where

B is the area of the hexagonal base

Find the area of the hexagonal base

The area of the regular hexagon is equal to the area of six equilateral triangles

we have

substitute

The surface area is equal to

the answer is b.

step-by-step explanation:

by the trigonometric ratio tangent, tangent equals opposite divided by adjacent.

therefore, tan(50) equals ac/3

multiply each side by 3 to get: ac=3tan(50)

the answer is b.