contestada

A new toy comes in the shape of a regular hexagonal pyramid. The base has side lengths of 10 inches and the apothem is 5āˆš3 inches. If the surface area is 420 + 150āˆš3 square inches, what is the slant height?
A. 11 inches
B. 14 inches
C. 7 inches
D. 28 inches

Relax

Respuesta :

akposevictor

The slant height of the hexagonal pyramid is: B. 14 inches.

What is the Area of a Regular Hexagon?

Area of a regular hexagon = 3āˆš3/2(sĀ²)

First, find the area of the regular hexagon:

Area = 3āˆš3/2(sĀ²) = 3āˆš3/2(10Ā²) = 150āˆš3 in.Ā².

Surface area is given as 420 + 150āˆš3 in.Ā².

Area of the 6 triangles = surface area - area of hexagonal base = 420 + 150āˆš3 - 150āˆš3

Area of the 6 triangles = 420 in.Ā²

Area of 1 triangle = 420/6 = 70 in.Ā²

Use the area of a triangle to find the slant height (h):

70 = 1/2(10)(h)

2(70) = 10(h)

140/20 = h

h = 14 in.

The answer is B. 14 inches.

Learn more about the area of regular hexagon on:

https://brainly.com/question/2919364

#SPJ1

Otras preguntas