A regulare pyramid has a base length of 10m a side length of 18m and a height of 5sqr3
Find the surface area of the regular pyramid shown to the nearest whole number?
(Choose 1 response)
810 m2 810 m2 740 m2 740 m2 775 m2 775 m2 800 m2
To find the surface area of a regular pyramid, we use the formula:
Surface Area = (1/2) * base perimeter * slant height + base area
First, calculate the base perimeter:
Base perimeter = 4 * base length = 4 * 10m = 40m
Now, calculate the slant height using the Pythagorean theorem:
slant height = sqrt((height)^2 + (base length / 2)^2)
slant height = sqrt((5sqrt(3))^2 + (10/2)^2)
slant height = sqrt(75 + 25)
slant height = sqrt(100) = 10m
Now, calculate the base area:
Base area = base length^2 = 10^2 = 100m^2
Plug these values into the surface area formula:
Surface Area = (1/2) * 40m * 10m + 100m^2
Surface Area = 200m + 100m^2
Surface Area = 300m^2
Therefore, the surface area of the regular pyramid is 300 m^2.
Among the given answer choices, the closest whole number is 300 m2.