The formula for the surface area of a square pyramid is given by:
SA = l² + 2lh
Where:
SA = Surface area
l = Length of the base
h = Height of the pyramid
We are given that the length of the base (l) is 40 in and the surface area (SA) is 2800 in².
Substituting these values into the formula, we have:
2800 = 40² + 2(40)(h)
Simplifying the equation:
2800 = 1600 + 80h
Subtracting 1600 from both sides:
1200 = 80h
Dividing both sides by 80:
15 = h
Therefore, the height of the pyramid is 15 in. The slant height (l) can be found using the Pythagorean theorem:
l² = h² + (1/2l)²
Substituting the values we know:
l² = 15² + (1/2(40))²
l² = 225 + 400/4
l² = 225 + 100
l² = 325
Taking the square root of both sides:
l = √325
l ≈ 18.03
Therefore, the slant height of the pyramid is approximately 18.03 in.
Use the formula for the surface area of a square pyramid to solve for the slant height if the length of the base is 40 in the sa equals 2,800 in square
7 answers
Wrong
I apologize for the mistake. Let's correct it.
The formula for the surface area of a square pyramid is:
SA = l² + 2lh
We are given that the length of the base (l) is 40 in and the surface area (SA) is 2800 in².
2800 = 40² + 2(40)(h)
2800 = 1600 + 80h
1200 = 80h
h = 1200/80
h = 15 in
Now, let's find the slant height (s) using the Pythagorean theorem:
s² = l² + h²
s² = 40² + 15²
s² = 1600 + 225
s² = 1825
s ≈ √1825
s ≈ 42.77 in
Therefore, the slant height of the square pyramid is approximately 42.77 in.
The formula for the surface area of a square pyramid is:
SA = l² + 2lh
We are given that the length of the base (l) is 40 in and the surface area (SA) is 2800 in².
2800 = 40² + 2(40)(h)
2800 = 1600 + 80h
1200 = 80h
h = 1200/80
h = 15 in
Now, let's find the slant height (s) using the Pythagorean theorem:
s² = l² + h²
s² = 40² + 15²
s² = 1600 + 225
s² = 1825
s ≈ √1825
s ≈ 42.77 in
Therefore, the slant height of the square pyramid is approximately 42.77 in.
Wrong answer again try again
I apologize for the repeated mistakes. Let's try solving it again.
The formula for the surface area of a square pyramid is:
SA = l² + 2lh
We are given that the length of the base (l) is 40 in and the surface area (SA) is 2800 in².
2800 = 40² + 2(40)(h)
2800 = 1600 + 80h
1200 = 80h
h = 1200/80
h = 15 in
Now, let's find the slant height (s) using the Pythagorean theorem:
s² = l² + h²
s² = 40² + 15²
s² = 1600 + 225
s² = 1825
s = √1825
s ≈ 42.77 in
Therefore, the slant height of the square pyramid is approximately 42.77 in.
The formula for the surface area of a square pyramid is:
SA = l² + 2lh
We are given that the length of the base (l) is 40 in and the surface area (SA) is 2800 in².
2800 = 40² + 2(40)(h)
2800 = 1600 + 80h
1200 = 80h
h = 1200/80
h = 15 in
Now, let's find the slant height (s) using the Pythagorean theorem:
s² = l² + h²
s² = 40² + 15²
s² = 1600 + 225
s² = 1825
s = √1825
s ≈ 42.77 in
Therefore, the slant height of the square pyramid is approximately 42.77 in.
Your answer for the third time's wrong the right answer is 15 in
I apologize for the repeated mistakes. You are correct, the correct answer for the slant height of the square pyramid is indeed 15 in. Thank you for pointing out the error.
1 answer