Understanding the Area of a Segment in a Circle

The video tutorial from Moomoomath explains how to find the area of a segment of a circle. A segment is defined as the area outside a chord within a sector of a circle, resembling a pizza crust. The process involves calculating the area of the entire sector using the formula (angle/360) * π * r² and then subtracting the area of the triangle formed by the chord. The example provided uses a right triangle with a 90-degree angle and a radius of 6 units. The tutorial concludes with tips on obtaining exact and approximate values for the segment area.

What is a segment in a circle?

• The entire circle

• The area outside a chord

• The area inside a chord

• The circumference of the circle

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CCSS.HSG.C.B.5

How do you find the area of a segment?

• By dividing the area of the circle by two

• By subtracting the area of the triangle from the sector

• By adding the area of the sector and the triangle

• By multiplying the radius by the chord length

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CCSS.HSG.C.B.5

What is the formula for the area of a sector?

• Measure over 360 times PI R squared

• PI R squared

• Base times height

• 2 PI R

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CCSS.8.G.A.5

In the example, what is the angle of the triangle?

• 45 degrees

• 90 degrees

• 60 degrees

• 120 degrees

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CCSS.HSG.C.B.5

What is the area of the sector in the example?

• 18 PI

• 9 PI

• 36 PI

• 6 PI

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CCSS.6.G.A.1

How is the area of the triangle calculated in the example?

• Measure over 360 times PI R squared

• Base times height

• PI times radius squared

• One-half base times height

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CCSS.HSG.C.B.5

What is the exact area of the segment before approximation?

• 6 PI - 9

• 36 PI - 18

• 18 PI - 9

• 9 PI - 18

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CCSS.HSG.C.B.5

What is the approximate area of the segment?

• 15.67 units squared

• 10.27 units squared

• 12.34 units squared

• 8.45 units squared

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CCSS.7.G.B.4

What is the radius used in the example?

• 7 units

• 6 units

• 5 units

• 4 units

What is the purpose of using a calculator in the final step?

• To find the exact area

• To calculate the circumference

• To find the approximate area

• To verify the radius