The roof of a building is shaped like a square pyramid, with a base of 18m by 18m. If the slant height of the roof is 12m and roofing costs 5.75m2, how much will it cost for roofing material?
The lateral surface area of a pyramid (the slanted sides) is the perimeter of the base P multiplied by the slant height H and divided by two, or
A(lateral) = PH/2
Finally multiply by the price per metre^2 to get the price.
so theres 4 sides to a pyramid does that mean each side is 18m?
Exactly!
The perimeter of the square base is therefore 4*18.
Useful information:
"18m x18m " is a short form for "each side of a square is 18m"
To find the cost of the roofing material, we first need to calculate the total surface area of the roof.
The surface area of a square pyramid can be calculated by finding the sum of the base area and the lateral area. The base area of the pyramid is simply the area of the square base, which is found by multiplying the length of one side by itself:
Base Area = (18m) * (18m) = 324m²
The lateral area of the pyramid includes the four triangular faces. Each face is an isosceles triangle, with the base as one side of the square base and the slant height as the height of the triangle. We can calculate the area of one triangle and then multiply it by 4 to get the total lateral area:
Area of one triangle = (1/2) * base * height
= (1/2) * (18m) * (12m)
= 108m²
Total Lateral Area = 4 * 108m² = 432m²
Now, we can find the total surface area by adding the base area and the lateral area:
Total Surface Area = Base Area + Lateral Area
= 324m² + 432m²
= 756m²
Finally, we can calculate the cost of the roofing material by multiplying the surface area by the cost per square meter:
Roofing Cost = Total Surface Area * Cost per square meter
= 756m² * $5.75/m²
= $4,347
Therefore, it will cost $4,347 for the roofing material.