Use the formula for the surface area of a square pyramid to solve for the slant height if the length of the base is 40in and SA equals 2800 inches squared
The formula for the surface area of a square pyramid is given by:
SA = B + (1/2)Pl
Where:
SA is the surface area
B is the area of the base
P is the perimeter of the base
l is the slant height
In this case, we are given that the length of the base is 40in and the surface area is 2800in². We can proceed to solve for the slant height.
First, we need to find the area of the base (B) and the perimeter of the base (P). Since the base is a square, all sides are equal in length.
The area of a square is found by squaring the length of one side, so:
B = 40^2 = 1600in²
The perimeter of a square is found by multiplying the length of one side by 4, so:
P = 4 * 40 = 160in
Now we can substitute these values into the formula:
2800 = 1600 + (1/2)(160)(l)
Multiplying the terms:
2800 = 1600 + 80l
Rearranging the equation:
80l = 2800 - 1600
80l = 1200
Finally, we solve for l:
l = 1200 / 80
l = 15
Therefore, the slant height of the square pyramid is 15 inches.
To solve for the slant height of a square pyramid, we can use the following formula for the surface area (SA):
SA = base area + (0.5 × perimeter of base × slant height)
Given that the length of the base (s) is 40 inches and the surface area (SA) is 2800 square inches, we can substitute these values into the formula:
2800 = s^2 + (0.5 × s × slant height)
We can now rearrange the equation to solve for the slant height.
2800 - s^2 = 0.5 × s × slant height
Let's plug in the value of the base length:
2800 - 40^2 = 0.5 × 40 × slant height
2800 - 1600 = 20 × slant height
1200 = 20 × slant height
To find the slant height, divide both sides of the equation by 20:
1200/20 = slant height
The slant height is therefore 60 inches.