Dynamic Activity

Surface and Lateral Areas of Pyramids and Cones

Take note Theorem 11-3: Lateral and Surface Areas of a Pyramid

The lateral area of a regular pyramid is half the product of the perimeter p of the base and the slant height l of the pyramid.

L.A. = 1 2 p l cap l.cap a. , equals , 1 half , p l

The surface area of a regular pyramid is the sum of the lateral area and the area B of the base.

S.A. = L.A. + B cap s.cap a. , equals , cap l.cap a. , plus b

Problem 1 Finding the Surface Area of a Pyramid

What is the surface area of the hexagonal pyramid?

S .A . = L .A . + B Use the formula for surface area .   = 1 2 p l + 1 2 a p Substitute the formulas for L .A . and  B .   = 1 2 ( 36 ) ( 9 ) + 1 2 ( 3 3 ) ( 36 ) Substitute .   ≈ 255.5307436 Use a calculator . table with 4 rows and 3 columns , row1 column 1 , cap s .cap a . , column 2 equals cap l .cap a . plus b , column 3 cap usetheformulaforsurfacearea . . , row2 column 1 , , column 2 equals , 1 half , p l plus , 1 half , eh p , column 3 cap substitutetheformulasforcap l . .cap a , .and b . , row3 column 1 , , column 2 equals , 1 half . open 36 close . open 9 close , plus , 1 half . open , 3 square root of 3 , close . open 36 close , column 3 cap substitute . . , row4 column 1 , , column 2 almost equal to . 255.5307436 , column 3 cap useacalculator . . , end table

The surface area of the pyramid is about 256  in . 2 . 256 , in , . squared , .

✓ Got It?

1. 1. A square pyramid has base edges of 5 m and a slant height of 3 m. What is the surface area of the pyramid?
   2. Reasoning Suppose the slant height of a pyramid is doubled. How does this affect the lateral area of the pyramid? Explain.