Question

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 of the following responses)
810 m2 810 m2 740 m2 740 m2 775 m2 775 m2 800 m2

Answer 1

To find the surface area of a regular pyramid, we need to calculate the area of the base and the area of the four triangular faces.

First, let's calculate the area of the base:
Area of base = length x width = 10m x 10m = 100m^2

Next, let's calculate the area of each triangular face:
We know that the side length of the regular pyramid is 18m, and the height of each triangular face is given as 5√3m.
Using the formula for the area of an equilateral triangle: A = 0.5 x base x height
Area of each triangular face = 0.5 x 18m x 5√3m = 45√3m^2

There are 4 triangular faces in total, so the total surface area of the pyramid is:
Surface area = area of base + 4 x area of triangular face
Surface area = 100m^2 + 4(45√3m^2)
Surface area = 100m^2 + 180√3m^2
Surface area ≈ 100m^2 + 310m^2
Surface area ≈ 410m^2

Therefore, the surface area of the regular pyramid is approximately 410m^2. To the nearest whole number, the surface area is 410m^2.

Therefore, the closest option given is 410 m2.