Finding Surface Areas and Volumes of Pyramids Lesson 70 Finding Surface Areas and Volumes of Pyramids

Vocabulary of a Pyramid Vertex is the common point of all the lateral faces Base is the face opposite the vertex Regular Pyramid has a reg. polygon for a base and the lateral faces are congruent triangles Slant height (l) of a reg. pyramid is the height of the lateral face Height of the pyramid (altitude) is ⊥ from the vertex to the plane containing the base

Formulas Lateral Area- ½ perimeter of the base times the slant height. L= 1 2 P l Surface Area- Lateral area plus the area of the base. S = L + B Volume- one third area of the base times the altitude. 𝑉= 1 3 𝐵ℎ

Find surface area & volume L= 1 2 P l L= 1 2 4 16 17 L= 544 in2 S= L + B S= 544 + 162 S= 800 in2 𝑉= 1 3 𝐵ℎ 𝑉= 1 3 256 15 𝑉= 1280 in3

How would you find the slant height? l = 𝑎 2 + 𝑏 2 l = 7 2 + 24 2 l = 625 l =25 Did you remember this triple? That’s okay, I didn’t either.

Questions? I tried to keep this simple and short. You might have to estimate or do some more problem solving to find unknown dimensions.