What is the surface area of a square pyramid with base length on 10 cm and slant height of 20 cm
To find the surface area of a square pyramid, we need to calculate the area of the base and the area of each triangular face.
The area of the base of a square pyramid is given by the formula:
Base Area = (side length)^2
In this case, the base length is 10 cm, so the base area is:
Base Area = 10 cm * 10 cm = 100 cm^2
The area of each triangular face of a square pyramid is given by the formula:
Face Area = (1/2) * (base length) * (slant height)
In this case, the base length is 10 cm and the slant height is 20 cm, so the face area is:
Face Area = (1/2) * 10 cm * 20 cm = 100 cm^2
Since a square pyramid has 4 triangular faces, the total surface area is obtained by adding the area of the base and the areas of the 4 triangular faces:
Total Surface Area = Base Area + 4 * Face Area = 100 cm^2 + 4 * 100 cm^2 = 100 cm^2 + 400 cm^2 = 500 cm^2
Therefore, the surface area of the square pyramid is 500 cm^2.
To find the surface area of a square pyramid, you need to calculate the area of the base and the area of the four triangular faces.
First, let's find the area of the base. Since the base of a square pyramid is a square, we can use the formula for the area of a square, which is side length squared.
Area of the base = (side length)^2
Given that the base length is 10 cm, the area of the base would be:
Area of the base = (10 cm)^2 = 100 cm^2
Next, let's find the area of the four triangular faces. The formula for the area of a triangle is 1/2 multiplied by the base multiplied by the height.
Since the base of each triangular face is the same as the base length of the square pyramid (10 cm), and the slant height is given as 20 cm, we can calculate the height of each triangular face using the Pythagorean theorem.
The height can be found using the equation:
Height = √(slant height^2 - (1/2 * base length)^2)
Height = √(20 cm^2 - (1/2 * 10 cm)^2)
Height = √(20 cm^2 - 25 cm^2)
Height = √(5 cm^2)
Height = 2.236 cm (rounded to three decimal places)
Now that we have the height, we can find the area of each triangular face:
Area of each triangular face = 1/2 * (base length) * (height)
Area of each triangular face = 1/2 * 10 cm * 2.236 cm
Area of each triangular face = 11.18 cm^2 (rounded to two decimal places)
Since there are four triangular faces, the total area of the triangular faces is:
Total area of the triangular faces = 4 * 11.18 cm^2 = 44.72 cm^2
Finally, to find the total surface area of the square pyramid, add the area of the base and the area of the four triangular faces:
Total surface area of the square pyramid = Area of the base + Total area of the triangular faces
Total surface area = 100 cm^2 + 44.72 cm^2
Total surface area = 144.72 cm^2
Therefore, the surface area of the square pyramid is 144.72 cm^2.