Area of a Segment

Front

What is the area of a sector formula?

Back

Area = (θ/360) × πr², where θ is the central angle in degrees and r is the radius.

Front

How do you find the area of a segment?

Back

Area of a segment = Area of the sector - Area of the triangle formed by the radius and the chord.

Front

What is a sector in a circle?

Back

A sector is a portion of a circle enclosed by two radii and the arc between them.

Front

What is a segment in a circle?

Back

A segment is the area of a circle that is 'cut off' from the rest of the circle by a chord.

Front

If the radius of a circle is 5 units and the central angle is 60 degrees, what is the area of the sector?

Back

Area = (60/360) × π(5)² = (1/6) × 25π ≈ 13.1 square units.

Front

What is the relationship between the arc length and the area of a sector?

Back

Arc length = (θ/360) × 2πr; the area of the sector can be derived from the arc length.

Front

What is the formula for the area of a triangle formed by two radii and a chord?

Back

Area = 1/2 × base × height, where the base is the chord and height is the perpendicular from the center to the chord.

Front

How do you convert radians to degrees?

Back

Degrees = Radians × (180/π).

Front

What is the area of a circle formula?

Back

Area = πr², where r is the radius.

Front

If the radius of a circle is 10 units, what is the area of the circle?

Back

Area = π(10)² = 100π ≈ 314.16 square units.