What is the surface area of a pyramid height of 4.5in. and base of 5in.?
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To find the surface area of a pyramid, you need to know the base area and the lateral area. The base area is the area of the base, and the lateral area is the sum of the areas of the triangular faces.
Here's how to find the surface area of a pyramid with a height of 4.5 inches and a base of 5 inches:
1. Start by calculating the base area, which is given by the formula: base area = 0.5 * base length * base width. In this case, the base length and width are both 5 inches. So, the base area = 0.5 * 5 * 5.
2. Calculate the lateral area, which is the sum of the areas of the triangular faces. Each triangular face has a base that is equal to the base length (5 inches) and a height that is equal to the overall height of the pyramid (4.5 inches). The area of each triangular face is given by the formula: triangle area = 0.5 * base length * height.
Therefore, the lateral area = 4 * (0.5 * 5 * 4.5), as there are 4 triangular faces on a pyramid.
3. Add the base area and the lateral area to find the total surface area: surface area = base area + lateral area.
Putting it all together, the surface area of the pyramid is:
surface area = (0.5 * 5 * 5) + (4 * (0.5 * 5 * 4.5))
= (0.5 * 25) + (4 * 11.25)
= 12.5 + 45
= 57.5 square inches.
Hence, the surface area of the pyramid with a height of 4.5 inches and a base of 5 inches is 57.5 square inches.