Question

WORTH 99 POINTS!

Answer 1

The general formula for the lateral surface area of a regular pyramid is:
$A= \frac{1}{2} *p*l$
Where:
p=perimeter of a base
l=slant height

a.
a=3ft
l=4ft
p=5*a=5*3=15ft
$A= \frac{1}{2} *15*4=30 ft^{2}$

b.
a=2.5ft
l=4ft
p=6*a=6*2.5=15ft
$A= \frac{1}{2} *15*4=30 ft^{2}$

c.
a=1.9ft
l=4ft
p=8*a=8*1.9=15.2ft
$A= \frac{1}{2} *15.2*4=30.4 ft^{2}$

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:
$A= \frac{1}{4} *n* a^{2}*cot( \frac{180}{n} )$

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

Answer 2

Hello!

A) 30ft^2

B) 30ft^2

C) 30.4ft^2

D) I don't know this sorry :/

I hope it helps!