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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

Find the surface area of the regular hexagonal pyramid Round your answer to the nearest hundredth A 6918 m2 B 7918 m2 C 8918 m2 D 9918 m2 class=

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carlosego

Answer: OPTION B

Step-by-step explanation:

 Use the following formula:

[tex]SA=\frac{pl}{2}+B[/tex]

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

The perimeter is:

[tex]p=6*s=6*3m=18m[/tex]

Where s is the lenght of a side.

The slant height is given:

[tex]l=6,2m[/tex]

The area of the base is:

[tex]B=\frac{3\sqrt{3}s^2}{2}=\frac{3\sqrt{3}(3m)^2}{2}=23.382m^2[/tex]

Where s is the length of a side.

Substitute values. Then, the result is:

[tex]SA=\frac{(18m)(6.2m)}{2}+23.382m^2=79.18m^2[/tex]

alinakincsem

Answer:

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

Step-by-step 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:

[tex]\frac{PI}{2} +B[/tex]

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

Perimeter of base = [tex]3 \times 6[/tex] = 18 m^2

Base area (area of hexagon) = [tex]\frac{3\sqrt{3} }{2} a^2[/tex] =  [tex]\frac{3\sqrt{3} }{2} 3^2[/tex] = 23.38 m^2

Surface area of hexagonal pyramid = [tex]\frac{18 \times 6.2}{2} +23.38[/tex] = 79.18 m^2

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