Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18 Show your work.
To calculate the surface area of a square pyramid, we need to find the area of the base and add to it the area of the four triangular faces.
1. Area of the base:
Since the base is a square, the area of the base is calculated by squaring the base length.
Area of the base = (12)^2 = 144 square units
2. Area of each triangular face:
The formula for the area of a triangle is (1/2) * base * height. In this case, the base of the triangle is the side length of the square base (12) and the height is the slant height of the pyramid (18).
Area of each triangular face = (1/2) * 12 * 18 = 108 square units
3. Total surface area:
Now we add the area of the base to the total area of the four triangular faces.
Total surface area = Area of base + 4 * Area of each triangular face
Total surface area = 144 + 4 * 108
Total surface area = 144 + 432
Total surface area = 576 square units
Therefore, the surface area of the square pyramid is 576 square units.
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To find the surface area of a square pyramid, you need to first figure out the area of the base and then add the area of the four triangle sides.
1. Find the area of the base:
Since the base is a square, we square the base length which is 12.
Base area = 12 x 12 = 144 square units
2. Calculate the area of each triangle side:
The formula for the area of a triangle is (1/2) x base x height. The base of each triangle is 12 (which is the side of the square base) and the height is 18 (the slant height of the pyramid).
Triangle area = (1/2) x 12 x 18 = 108 square units
3. Add it all up:
Now we add the area of the base to the total area of all four triangle sides.
Total surface area = Base area + 4 x Triangle area
Total surface area = 144 + 4 x 108
Total surface area = 144 + 432
Total surface area = 576 square units
So, the surface area of the square pyramid is 576 square units.