12.3 SA of Cones and Pyramids

Similarly to 12.2, we need to separate into base and lateral area.

Notice with a cone, we only have one base (circle)

The lateral area is similar to that of a cylinder, but we won't use circumference, like we did for the cylinders.

Base Area: It's a circle, so:

Lateral Area:  $\pi rl$  

 $l$  represents the slant height!!

Remember to add the base and lateral areas together at the end!

Can we find the slant height somehow? (What kind of triangle does it make?)

Use pythagorean theorem to find the hypotenuse (slant height)!

 $4^2+9^2=$  

 $\sqrt{97}$  

Now you have this slant height, find the lateral area

Add this LA to the base area

SA = 174.02

Base Area: Find the area of the base; in this case, it's a square (might not always be a square though!)

Lateral Area: Just like cones, we are still using the 'slant' height. Once we find the slant height, we multiple it to our perimeter of our base, and then divide by two.

Base Area: It's a square, so:  $l\times w$  

Lateral Area:  $\frac{pl}{2};\ p=perimeter,\ l=slant\ height$   $SA=70in^2$