Surface Area of Pyramids and Cones

Surface Area and Lateral Area of Pyramids and Cones

Slant Height

slant height - the distance measured along the lateral face from the top of the pyramid to the edge of the base.

Lateral Area of Pyramids

 $L=\frac{nbs}{2}$  

n is the number of sides on the base shape
b is the length of the base shape
s is the slant height

A pentagonal pyramid has a 10 mm pentagonal side length and a slant height of 16 mm. What is the lateral area?

• n = 5

• b = 10 mm

• s = 16 mm

•  $L=\frac{\left(5\right)\left(10\right)\left(16\right)}{2}=400\ mm^2$  

Multiple Choice

What is the lateral area of the pyramid?

• 384 cm²

• 256 cm²

• 640 cm²

• 28 cm²

Surface Area

 $L=\frac{nbs}{2}+B$  

B is the area of the base shape

A pentagonal pyramid has a 230 square mm base area, a 10 mm pentagonal side length and a slant height of 16 mm. What is the surface area?

• n = 5

• b = 10 mm

• s = 16 mm

• B = 230 square mm

•  $SA=\frac{\left(5\right)\left(10\right)\left(16\right)}{2}+230=630\ mm^2$  

Fill in the Blanks

A hexagonal pyramid has a base area of 288 cm², a side length of 12 cm, and a height of 22 cm. What is the surface area of the pyramid?

Lateral and Surface Area of a Cone

Lateral Area
 $L=\pi rs$  

Surface Area

 $SA=\pi rs+\pi r^2$  

A cone has a slant height of 23.4 in and a diameter of 16 in. What is the lateral area of the cone?

s = 23.4
d = 16
r = 8

 $L=\pi\left(8\right)\left(23.4\right)=588.1\ in^2$  

Multiple Choice

Determine the lateral area of the cone shown.

• 345.3 ft²

• 690.5 ft²

• 219.9 ft²

• 769.3 ft²

A cone has a slant height of 23.4 in and a diameter of 16 in. What is the surface area of the cone?

s = 23.4
d = 16
r = 8

 $L=\pi\left(8\right)\left(23.4\right)+\pi\left(8\right)^2=588.1\ +201.1=789.2\ in^2$  

Multiple Choice

Find the surface area of the figure.

Round your answer to the nearest hundredth.

• 542.87 $mm^2$

• 271. 44 $mm^2$

• 221.06 $mm^2$

• 442.12 $mm^2$