The surface area of a square pyramid can be calculated by finding the area of the base and adding the areas of the four triangular faces.
The area of the base is found by squaring the length of one side of the square base:
Area of base = (10 cm)^2 = 100 cm^2
The area of each triangular face is found by multiplying half the base length (since it is a right triangle) by the slant height:
Area of each triangular face = (1/2)(10 cm)(20 cm) = 100 cm^2
Since there are four triangular faces, the total area of the four triangular faces is:
Total area of triangular faces = 4 * (100 cm^2) = 400 cm^2
Finally, to find the surface area of the square pyramid, we add the area of the base and the total area of the triangular faces:
Surface area = Area of base + Total area of triangular faces = 100 cm^2 + 400 cm^2 = 500 cm^2
Therefore, the surface area of the square pyramid is 500 cm^2.
What is the surface area of a square pyramid with base length of 10 cm and slant height of 20 cm?(1 po
3 answers
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 in2
The formula for the surface area of a square pyramid is:
Surface area = Base area + (1/2) * Perimeter of base * Slant height
In this case, we know the length of the base (40 in.) and the surface area (2,800 in^2), and we need to solve for the slant height.
Let's start by finding the base area:
Base area = (40 in.)^2 = 1,600 in^2
We can substitute the values we know into the formula and solve for the slant height:
2,800 in^2 = 1,600 in^2 + (1/2) * Perimeter of base * Slant height
2,800 in^2 = 1,600 in^2 + (1/2) * (4 * 40 in.) * Slant height
2,800 in^2 = 1,600 in^2 + 320 in. * Slant height
2,800 in^2 = 1,600 in^2 + 320 in^2 * Slant height
2,800 in^2 - 1,600 in^2 = 320 in^2 * Slant height
1,200 in^2 = 320 in^2 * Slant height
Slant height = 1,200 in^2 / 320 in^2
Slant height = 3.75 in
Therefore, the slant height of the square pyramid is 3.75 inches.
Surface area = Base area + (1/2) * Perimeter of base * Slant height
In this case, we know the length of the base (40 in.) and the surface area (2,800 in^2), and we need to solve for the slant height.
Let's start by finding the base area:
Base area = (40 in.)^2 = 1,600 in^2
We can substitute the values we know into the formula and solve for the slant height:
2,800 in^2 = 1,600 in^2 + (1/2) * Perimeter of base * Slant height
2,800 in^2 = 1,600 in^2 + (1/2) * (4 * 40 in.) * Slant height
2,800 in^2 = 1,600 in^2 + 320 in. * Slant height
2,800 in^2 = 1,600 in^2 + 320 in^2 * Slant height
2,800 in^2 - 1,600 in^2 = 320 in^2 * Slant height
1,200 in^2 = 320 in^2 * Slant height
Slant height = 1,200 in^2 / 320 in^2
Slant height = 3.75 in
Therefore, the slant height of the square pyramid is 3.75 inches.
1 answer