Head First 2D Geometry

226 Chapter 5

sectors are like triangles

If you pretended that a slice (sector) was a triangle, you could work

out the area of that slice and then add up all the slices.

Each sector (slice) is a triangle (kind of)

A sector of a circle isn’t actually a triangle with three straight edges,

but it’s pretty close. You can find the approximate area of that sector

by using the radius of the circle as the triangle height, and the arc

length as the triangle base.

Which technique from your Geometry Toolbox could help

you work out the pizza areas approximately?

Solution

Triangle area

= 1/2 base x

height

Similarity &

congruence

Angles in a

quadrilateral

add up to 360º.

Height = radius

Base = arc length

A sector is like a

triangle with a

curved base.

Exactly equal

The length of the base is

pretty close to the length

of the arc of this sector.

Approximately

you are here 4 227

circles

Geometry Detective

8"

This pizza has a diameter of 8 inches.

Using radius to stand in for height, and arc length

to stand in for base, use the triangle area formula

to investigate how you can approximate the circle

area.…

1. By chopping the pizza base into 6 equal slices

3. By chopping the pizza base into 30 equal slices

2. By chopping the pizza base into 10 equal slices

What do you notice as you chop it into

more and more slices? ...