1) Given the side of a square pyramid is 6cm and the altitude is 4cm calculate the surface area.
2) Given the side of a square pyramid is 12cm and the altitude is 8cm calculate the surface area.
3) Given the side of a square pyramid is 18cm and the altitude is 12cm calculate the surface area.
4) Given the side of a square pyramid is 24cm and the altitude is 16cm calculate the surface area.
5) Given the side of a square pyramid is 30cm and the altitude is 20cm calculate the surface area.
6) Given the side of a square pyramid is 36cm and the altitude is 24cm calculate the surface area.
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What I’m having trouble with is which formula do I use to solve those problems. For example: if I was to do,
Given the side of a square pyramid is 2cm, and the slant height is 3 cm, find the surface area of the pyramid.
I’d use this formula SA=S2(squared) + 2S.
This person probably graduated in 2011 so why are you responding in 2018?
This person is probably out of college!
a pyramid has a volume of 230 square feet . what is the hieght of the pyramid if the base of the pyramid has an area of 30 square feet ?
5.3
7.3
Bro really commented because I was born "Skull emoticon"
To calculate the surface area of a square pyramid, you can use the formula:
SA = S^2 + 2S√(S^2/4 + H^2)
Where:
SA is the surface area
S is the length of one side of the square base
H is the altitude (height) of the pyramid
Now, let's solve the problems you provided step by step:
1) Given S = 6cm and H = 4cm:
SA = 6^2 + 2(6)√(6^2/4 + 4^2)
= 36 + 12√(36/4 + 16)
= 36 + 12√(36/4 + 256/16)
= 36 + 12√(9 + 16)
= 36 + 12√25
= 36 + 12(5)
= 36 + 60
= 96 cm^2
2) Given S = 12cm and H = 8cm:
SA = 12^2 + 2(12)√(12^2/4 + 8^2)
= 144 + 24√(144/4 + 64)
= 144 + 24√(144/4 + 256/16)
= 144 + 24√(36 + 16)
= 144 + 24√52
≈ 144 + 24(7.211)
≈ 144 + 172.664
≈ 316.664 cm^2
3) Given S = 18cm and H = 12cm:
SA = 18^2 + 2(18)√(18^2/4 + 12^2)
= 324 + 36√(324/4 + 144)
= 324 + 36√(324/4 + 144/1)
= 324 + 36√(81 + 144)
= 324 + 36√225
= 324 + 36(15)
= 324 + 540
= 864 cm^2
4) Given S = 24cm and H = 16cm:
SA = 24^2 + 2(24)√(24^2/4 + 16^2)
= 576 + 48√(576/4 + 256)
= 576 + 48√(576/4 + 256/1)
= 576 + 48√(144 + 256)
= 576 + 48√400
= 576 + 48(20)
= 576 + 960
= 1536 cm^2
5) Given S = 30cm and H = 20cm:
SA = 30^2 + 2(30)√(30^2/4 + 20^2)
= 900 + 60√(900/4 + 400)
= 900 + 60√(900/4 + 400/1)
= 900 + 60√(225 + 400)
= 900 + 60√625
= 900 + 60(25)
= 900 + 1500
= 2400 cm^2
6) Given S = 36cm and H = 24cm:
SA = 36^2 + 2(36)√(36^2/4 + 24^2)
= 1296 + 72√(1296/4 + 576)
= 1296 + 72√(1296/4 + 576/1)
= 1296 + 72√(324 + 576)
= 1296 + 72√900
= 1296 + 72(30)
= 1296 + 2160
= 3456 cm^2
Remember to always double-check your calculations using a calculator to ensure accuracy.