Question

Find the surface area of the regular hexagonal pyramid. Round your answer to the nearest hundredth. A. 69.18 m^2 B. 79.18 m^2 C. 89.18 m^2 D. 99.18 m^2

Answer 1

The correct answer option is B. 79.18 m^2.

Explanation:

We are given a diagram of a regular hexagonal pyramid with height 5.6 m, slant height 6.2 m and base edge length 3m.

We know that the surface area of a regular hexagonal pyramid is given by:

`(PI)/(2) +B`

where P = perimeter of the base, I = slant height and B = base area.

Perimeter of base =
`3 * 6` = 18 m^2

Base area (area of hexagon) =
`(3√(3) )/(2) a^2` =
`(3√(3) )/(2) 3^2` = 23.38 m^2

Surface area of hexagonal pyramid =
`(18 * 6.2)/(2) +23.38` = 79.18 m^2

Answer 2

Answer: OPTION B

Explanation:

Use the following formula:

`SA=(pl)/(2)+B`

Where p is the perimeter of the base, l is the slant height and B is the area of the base.

The perimeter is:

`p=6*s=6*3m=18m`

Where s is the lenght of a side.

The slant height is given:

`l=6,2m`

The area of the base is:

`B=(3√(3)s^2)/(2)=(3√(3)(3m)^2)/(2)=23.382m^2`

Where s is the length of a side.

Substitute values. Then, the result is:

`SA=((18m)(6.2m))/(2)+23.382m^2=79.18m^2`