1. Warm Up Problem
Is this an arithmetic or geometric sequence? What is the next number in the sequence?
12, 27, 42, 57, …

2. Surface Area of Pyramids
Lesson 10-5

3. Objectives I can find the surface area of a pyramid.
I can define pyramid, lateral face, slant height, and vertex.

4. Vocabulary
pyramid – a 3D figure with at least 3 lateral faces that are triangles
lateral face – the triangular faces of a square pyramid are the lateral faces
slant height – the height of each lateral face
vertex – the intersection of the edges

6. Example 1
Find the surface area of the pyramid. Area of the base: 7 x 7 = 49 Area of each triangular side: 7 x 9 = 63 63/2 = 31.5 Find the sum: = 175cm²

7. Got It?
Find the surface area of each figure

8. Area of lateral faces: 4 x 5 ÷ 2 = 10
Example 2
Find the surface area of the pyramid.
Find the area of each face and add.
Area of base: 4 x 3.5 ÷ 2 = 7
Area of lateral faces: 4 x 5 ÷ 2 = 10
Sum: = 37ft²

9. Got It?
Find the surface area of each pyramid

10. Example 3
A pyramid puzzle has all sides that are equilateral triangles. Each triangle has side lengths of 8 centimeters. The slant height is 6.9cm. Find the surface area of the puzzle.
Each face has an area of
8 x 6.9 ÷ 2 = 27.6
So the surface area is 4 x 27.6
or 110.4cm²

11. Got It?
5. Pyramid-shaped gift boxes have square bases that measure 5 inches on each side. The slant height is 6.5 inches. How much cardboard is used to make each box?