Find the total surface area of a triangular shaped pyramid with a slant height of 16 units, base length of 8 units, and a height of 7 units.
Step 1. Find the lateral area of one side.
1/2(8 * 16 )= 64 units
Step 2. Multiply by the number of the sides.
64*3 = 192 units
Step 3. Find the area of the base
½ *( 8 * 7) = 28
Step 4. Add the lateral area and the base area together for the total surface area.
192 + 28 = 220 units squared
Slant Height =16 Units
Base Length= 8 units
Common Core Standard: 7.G.6 Seventh Grade Math
Geometry Tip: Slant height is not the same as the height of the pyramid. The slant height is the altitude of the lateral area of the side of the pyramid. The following video details how to find slant height of a pyramid.
Slant height of a Pyramid
Questions answered in this video...
What is the slant height of a pyramid?
What is the lateral area of a pyramid?
How is the slant height of a pyramid different than it's height?
Is slant height used to calculate total surface area of a pyramid?
Questions answered in this video...
What is the formula for finding the surface area of a pyramid?
What is slant height for a pyramid?
Is the base the same for all pyramids?
How do you find the perimeter of a pyramid?
How to find the surfave area of a pyramid
Hi Welcome to MooMooMath. Today we are going to look at how to find the surface area of a pyramid. What is a pyramid? A pyramid is a three dimensional figure with a base and an apex and a square pyramid and a pyramid is named by the shape of the base. We are going to look at the surface area and it is the material needed to cover the sides and the base. So we will take this pyramid and divide it up. The sides of each side of the pyramid is a triangle and the base is a square and I have separated those out. Now to find the surface area, I have to look at this figure. I have four sides so I have four triangles. If I can find the area of a triangle I can multiply by four and then I will add just one base to it. So let’s take and isolate this triangle. The triangle has a base of 6 and we need this height down the center of the face and that will be the height of the triangle. This measure is called the slant height. To find the slant height I will use the Pythagorean Theorem. Inside this pyramid I have a right triangle, and it is half of this base,half of the base is 3 and my height is 4 so I’m going to solve it by using the Pythagorean Theorem to find the slant height. I will use 3 squared plus 4 squared equals C squared. This is equal to (9 + 16 = 25) which is equal to 5 (the square root of 25 equals 5) so my slant height is 5. Now I’m going to find the area of the triangle which is equal to 1/2 b ∙h and our height is five so one half of 6 times 5 is 15 and I have 4 of these triangles so I will multiple this by four and this gives me the surface area of the sides which is the lateral area. This is 60 ( 15 x 4 =60) Now I’m going to add my base which is length times height because it is a square, so 6 times 6 is 36 so I add those two together and that gives me 96 square units. There you go, that is how you find the surface area of a pyramid. Take the area of one base and multiple by the number of faces and that gives us the lateral area and then we add one base and that gives us the surface area. Hope this was helpful.
A pyramid is a three dimensional figure that has a base and an apex.
The formula for finding the surface area of a pyramid will depend on the shape of the base.
For example, a pyramid with a rectangular shaped base will use length x width to find the area of the base,but a pyramid with a triangular shape will use 1/2 base x height