Determine the surface area of a pyramid with slant height 15 and a square base of side 10.
If we consider the net of a square-based pyramid, it is made up of one square and four identical isosceles triangles. As each side of the square has length 10, the area can be calculated by multiplying 10 by 10. This is equal to 100. Therefore, the area of the square is 100.
The area of any triangle can be calculated by multiplying the base by the height and then dividing by two. In this case, the base of each triangle is 10, the height of each triangle is 15 as the slant height of the pyramid was 15.
Substituting in these numbers tells us that the area of the triangle is equal to 10 multiplied by 15 divided by two. 10 multiplied by 15 is 150 and 150 divided by two is 75. This means that the area of each isosceles triangle is 75.
We can therefore calculate the total surface area by multiplying 75 by four and adding 100 as there are four triangles with area 75 and one square with area 100. Four multiplied by 75 is 300. Adding 100 to this gives us a total surface area of 400.
This means that the surface area of a pyramid with slant height 15 and a square base of side 10 is equal to 400.