To find the surface area of a regular pyramid, we need to find the area of the base and the area of the lateral faces and then add them together.
The base of the pyramid is a regular pentagon, so we need to find the area of a pentagon given the length of one side. The formula for the area of a regular pentagon is:
Area = (5/4) * s^2 * cot(π/5)
where s is the length of one side.
In this case, s = 10m, so:
Area = (5/4) * 10^2 * cot(π/5)
Area ≈ 130.9 m^2
Next, we need to find the area of the lateral faces. Each lateral face of a regular pyramid is a triangle. The formula for the area of a triangle is:
Area = (1/2) * base * height
In this case, the base of the triangle is the length of one side of the pentagon (10m) and the height can be found by using the Pythagorean theorem. The height of the triangle is the slant height (l), which can be found using the formula:
l = sqrt(h^2 + (s/2)^2)
where h is the height of the pyramid, which is given as 13m, and s is the length of one side of the base.
In this case:
l = sqrt(13^2 + (10/2)^2)
= sqrt(169 + 25)
= sqrt(194)
≈ 13.93 m
Now we can find the area of each triangle:
Area = (1/2) * 10 * 13.93
≈ 69.65 m^2
There are 5 lateral faces in a regular pentagonal pyramid, so the total area of the lateral faces is:
Total area = 5 * 69.65
≈ 348.25 m^2
Finally, we can find the total surface area by adding the area of the base and the area of the lateral faces:
Total surface area = 130.9 + 348.25
≈ 479 m^2
Therefore, the surface area of the regular pyramid is approximately 479 square meters.
For the following question find the surface area of the regular pyramid shown to the nearest whole number 10 m 13m 5 ^3
1 answer