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. and SA equals 2,800 in squared
My apologies for the mistake, let's try again.
The formula for the surface area (SA) of a square pyramid is:
SA = B + (0.5 × P × l)
where B is the area of the base, P is the perimeter of the base, and l is the slant height.
Given that the length of the base (B) is 40 in. and the surface area (SA) is 2,800 in^2, we can substitute these values into the formula:
2,800 = B + (0.5 × P × l)
The base of the square pyramid is a square, so the area (B) is given by the formula:
B = side length^2
Since the length of the base is 40 in., the area (B) is:
B = 40^2 = 1,600 in^2
Now we can rewrite the equation as:
2,800 = 1,600 + (0.5 × P × l)
Subtracting 1,600 from both sides:
1,200 = 0.5 × P × l
Dividing both sides by 0.5 × P:
l = 1,200 / (0.5 × P)
Since the length of the base is 40 in., the perimeter (P) is:
P = 4 × 40 = 160 in.
Substituting the value of P:
l = 1,200 / (0.5 × 160)
l = 1,200 / 80
l = 15 in.
Therefore, the slant height of the square pyramid is 15 inches.
The formula for the surface area (SA) of a square pyramid is:
SA = B + (0.5 × P × l)
where B is the area of the base, P is the perimeter of the base, and l is the slant height.
Given that the length of the base (B) is 40 in. and the surface area (SA) is 2,800 in^2, we can substitute these values into the formula:
2,800 = 40 + (0.5 × P × l)
Now we need to find the perimeter (P) of the base. Since it's a square pyramid, all four sides of the base are equal in length.
The perimeter of a square is given by the formula:
P = 4 × side length
Since the length of the base is 40 in., the perimeter (P) is:
P = 4 × 40 = 160 in.
Now we can rewrite the equation as:
2,800 = 40 + (0.5 × 160 × l)
2,800 = 40 + 80l
Subtracting 40 from both sides:
2,760 = 80l
Dividing both sides by 80:
l = 2,760 / 80
l = 34.5 in.
Therefore, the slant height of the square pyramid is 34.5 inches.