There are many different types of pyramids, and they differ in one way: the number of sides the base has. I will be talking
about 2 types, ones with equilateral triangle bases and ones with square bases. The triangle base one is technically called a tetrahedron,
and is one of my favorite 3D shapes. To find the area of a pyramid, find the area of all the sides, then add them.
The formula for the pyramid with a square base is (a*a)+(a*s*2) with a being the base length and s being the slant height.
In this picture, the base length is 16. However, the height given is not the slant height, it is the height of the
whole pyramid. To calculate the slant height, we can use Pythagoras' Therom to calculate the slant height. The square root of (82)+(242) is
approximatly 26.3, which we can enter into our formula to give us 1097.6 units squared.
Try It! (Square Pyramid)
Enter the values.
Show Your Work:
Surface Area (Equalateral Triangle Pyramid)
You should have read the top, so I should only have to give you the formula, which is b*h*2 with b being the base length
and h being the slant height. This is because the area of a triangle is b*h/2, so if we have 4 sides, it would be (b*h/2)*4, which can be simplified to
b*h*2. The area of the tetrahedron to the right is 8*18*2, which is 288 units squared.