Question

Find total area for the regular pyramid.

Answer 1

http://www.cliffsnotes.com/study_guide/Regular-Pyramids.topicArticleId-18851,articleId-18836.html


rather helpful

Answer 2

@jim_thompson5910

Answer 3

each triangle has an area of 4*6/2 = 12 square units

there are 6 of them, so the lateral surface area is 6*12 = 72 square units

Answer 4

you just need to find the area of the base to get the total surface area

Answer 5

Thats what I'm having problems with. I don't know how to find the base for a hexagonal pyramid.

Answer 6

let's rotate the 3D figure and look directly at the hexagonal base

Answer 7

if we do that, we get

Answer 8

now divide this hexagon up into triangles

Answer 9

each triangle is an equilateral triangle with side length of 4

Answer 10

so you can use this formula

A = (1/4)*sqrt(3)*s^2

where

s = side length

to find the area of each triangle

Answer 11

got 4sqrt3

Answer 12

that's the area of one triangle

but there are 6 of them (that are the same area)

so the hexagon has a total area of 6*4*sqrt(3) = 24*sqrt(3) square units

Answer 13

total surface area = (Base Area) + (Lateral Surface Area)

total surface area = (24*sqrt(3)) + (72)

total surface area = 24*sqrt(3) + 72

total surface area = 72 + 24*sqrt(3)

Answer 14

Thank you soo much!!

Answer 15

you're welcome