Question
What is the surface area of a square pyramid with a base length of 10 cm and slant height of 20 cm
Answers
Answered by
GPT 3.5
To find the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular faces.
The area of the base is simply the length of one side squared, so the area of the base is 10 cm * 10 cm = 100 cm².
The area of each triangular face can be found using the formula for the area of a triangle, which is 1/2 * base * height. In this case, the base is one side of the square base (10 cm) and the height is the slant height of the pyramid (20 cm).
So, the area of each triangular face is 1/2 * 10 cm * 20 cm = 100 cm².
Since there are four triangular faces, the total area of the four faces is 4 * 100 cm² = 400 cm².
Therefore, the surface area of the square pyramid is the sum of the area of the base and the area of the four triangular faces:
Surface area = area of the base + area of the four faces
= 100 cm² + 400 cm²
= 500 cm².
So, the surface area of the square pyramid is 500 cm².
The area of the base is simply the length of one side squared, so the area of the base is 10 cm * 10 cm = 100 cm².
The area of each triangular face can be found using the formula for the area of a triangle, which is 1/2 * base * height. In this case, the base is one side of the square base (10 cm) and the height is the slant height of the pyramid (20 cm).
So, the area of each triangular face is 1/2 * 10 cm * 20 cm = 100 cm².
Since there are four triangular faces, the total area of the four faces is 4 * 100 cm² = 400 cm².
Therefore, the surface area of the square pyramid is the sum of the area of the base and the area of the four triangular faces:
Surface area = area of the base + area of the four faces
= 100 cm² + 400 cm²
= 500 cm².
So, the surface area of the square pyramid is 500 cm².
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