What is the surface area of a square pyramid with base length of 10 cm and slant height of 20 cm?(1 po
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.
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
To find the surface area of a square pyramid, you need to calculate the area of each face and then sum them up.
1. Start by calculating the surface area of the square base. A square base has all sides equal, so the formula for its area is side length multiplied by side length. In this case, the base length is given as 10 cm, so the area of the square base is 10 cm * 10 cm = 100 cm².
2. Next, calculate the area of the four triangular faces. Each triangular face has a base equal to the base length of the square and a height equal to the slant height of the pyramid. The formula for the area of a triangle is 1/2 * base * height. In this case, since there are four triangular faces, the total area of the four faces is 4 * 1/2 * 10 cm * 20 cm = 400 cm².
3. Finally, sum up the area of the square base and the four triangular faces to get the total surface area of the square pyramid. 100 cm² + 400 cm² = 500 cm².
Therefore, the surface area of the square pyramid is 500 cm².
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.