Assignment: Circles: Area of Segments

CIRCLES: AREA OF SEGMENTS

In the previous lesson, we learned how to find the area of a sector of a circle. You will need that skill to be able to find the area of a segment of circle.

Objectives
- Find the area of unusual shapes using the areras of sectors and segments
- Find the area of a segment of a circle

Vocabulary
segment of a circle The part of a circle bounded by a chord and its arc.

Question #1MultipleChoice

A chord divides a circle into ___ segments.

one
two
three
four

Question #2

To find the area of the larger segment, ABY, we can either subtract the area of segment ABX from the area of the circle, or add the area of triangle AOB to the area of sector O-AYB.

Question #3

Express answer in exact form. Show all work for full credit.

A segment of a circle has a 120º arc and a chord of 8√3 in. Find the area of the segment.

Express answer in exact form. Show all work for full credit.

Find the area of one segment formed by a square with sides of 6" inscribed in a circle. (Hint: use the ratio of to find the radius of the circle.)

Question #4

Express answer in exact form. Show all work for full credit.

A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.

(Hint: remember Corollary 1--the area of an equilateral triangle is 1/4 s²√3

Question #5

Find the area of the shaded portion in the equilateral triangle with sides 6. Show all work for full credit. (Hint: Assume that the central point of each arc is its corresponding vertex.)

Question #6

Find the area of the shaded portion in the equilateral triangle with sides 6. Show all work for full credit. (Hint: Assume that the central point of each arc is its corresponding vertex.)

Area of Overlapping Circles

To find the area created by overlapping circles you will need to find the area of each segment created when the circles overlap. Take a look at the overlapping segments in circles B and A.

As you can see, circles B and A overlap each other creating an almond-shaped figure. This figure is created by two segments - one from circle A and one from circle B. Use radial lengths in each circle to define the size and shape of the figure. Draw in BC, BD, AC and AD.

Separate the circles so that you can clearly see the individual segments.

To find the area of this figure, you will need to find the area of each segment and then combine the areas.

Question #7

Find the area of the shaded portion intersecting between the two circles. Show all work for full credit.

Question #8

Find the area of the shaded portion. Show all work for full credit.

Question #9

Given: BC = 10 inches

AC = √50 inches

m∠CBD = 60°

m∠CAD = 90°

Calculate the exact area of the shaded region. Show all work for full credit.

Question #10

Find the area of segment CFD given the following information: radius = 8in, area of ΔCBD = 25.9in², and m∠CBD = 54°

Round your answer to the nearest hundredths if necessary.

4.26 in²
20.10 in²
3.23 in²
17.90 in²