Question

A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid

• 72 + 24^3 sq. units
• 96^3 sq. units
• 24 + 72^3 sq. units
• 24 + 96^3 sq. units

Answer 1

choice a

Explanation:

first need to find the apothem of hexagon. just take only the hexagon. apothem is the line joining center of hexagon to mid point of any side.

to calculate this, apply Pythagoras theorem. apothem will form right angle at the midpoint of side. and bisects the side of hexagon

2^2+apo^2 = radius of hexagon^2

here hexagon is regular. so radius = side = 4

apo^2 = 12

apo = 2√3

total area = 3ab+3bs

a = apothem = 2√3

b = side = 4

3ab = 24√3

s = slant ht = 6

3bs = 72

total area = 72+24√3