Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18. Show your work. (2 points) (Write like a 7th grader)
To calculate the surface area of a square pyramid, we need to find the base area and the area of each triangular face.
First, let's find the base area:
The formula for finding the area of a square is length x width. Since the base of the pyramid is a square, we use base length x base length.
Base Area = 12 x 12 = 144 square units
Next, let's find the area of one of the triangular faces:
The formula for finding the area of a triangle is 1/2 x base x height. The base of the triangle is the base length of the pyramid, which is 12. The height of the triangle is the slant height of the pyramid, which is 18.
Area of one triangular face = 1/2 x 12 x 18 = 108 square units
Since there are 4 triangular faces on a square pyramid, we multiply the area of one triangular face by 4 to get the total triangular face area:
Total triangular face area = 108 x 4 = 432 square units
Finally, to find the surface area of the square pyramid, we add the base area and the total triangular face area:
Surface Area = base area + total triangular face area
Surface Area = 144 + 432 = 576 square units
Therefore, the surface area of the square pyramid is 576 square units.
WAY SHORTER
Sure! Here's a shorter version:
Base area = 12 x 12 = 144 square units
Triangular face area = 1/2 x 12 x 18 = 108 square units
Total triangular face area = 108 x 4 = 432 square units
Surface area = base area + total triangular face area
Surface area = 144 + 432 = 576 square units
Therefore, the surface area of the square pyramid is 576 square units.