Question

WORTH 99 POINTS!

Please, I know it's long but I really need help! I just want the answers and tomorrow I plan to stay after in class for further understanding. Someone, please answer these questions!

Your friend is purchasing an umbrella with a slant height of 4 feet. There are a variety of such umbrellas to choose from.

a. A red umbrella is shaped like a regular pentagonal pyramid with a side length of 3 feet. Find the lateral surface area of the red umbrella.

b. A yellow umbrella is shaped like a regular hexagonal pyramid with a side length of 2.5 feet. Find the lateral surface area of the yellow umbrella.

c. A blue umbrella is shaped like a regular octagonal pyramid with a side length of 1.9 feet. Find the lateral surface area of the blue umbrella.

d. Based on lateral surface areas, would you suggest that your friend pick the umbrella that is her favorite color? Explain.

Answer 1

Hello!

A) 30ft^2

B) 30ft^2

C) 30.4ft^2

D) I don't know this sorry :/

I hope it helps!

Answer 2

The general formula for the lateral surface area of a regular pyramid is:

`A= (1)/(2) *p*l`
Where:
p=perimeter of a base
l=slant height

a.
a=3ft
l=4ft
p=5*a=5*3=15ft

`A= (1)/(2) *15*4=30 ft^(2)`

b.
a=2.5ft
l=4ft
p=6*a=6*2.5=15ft

`A= (1)/(2) *15*4=30 ft^(2)`

c.
a=1.9ft
l=4ft
p=8*a=8*1.9=15.2ft

`A= (1)/(2) *15.2*4=30.4 ft^(2)`

d.
Based on a lateral surface area the blue umbrella is best choice. But, the best umbrella overall is the one with the greatest base area. General formula for regular polygon is:

`A= (1)/(4) *n* a^(2)*cot( (180)/(n) )`

For pentagon:
A=15.48ft^2
For hexagon:
A=16.24ft^2
For octagon:
A=17.43ft^2
Blue umbrella is still best choice.