Geometry Honors - Areas of Circles and Sectors

Flashcards from Geometry Honors Lecture Notes - Chapters on Areas of Circles and Sectors. Topics include polygons, regular polygons, circumference and area of circles, arc length, sector area, geometric topics, and geometric probability.

What is a polygon?

The union of segments in a plane that intersect only at their endpoints, with no consecutive segments being collinear.

What is the perimeter of a polygon?

The sum of the lengths of the sides.

What is a diagonal of a polygon?

A segment joining nonconsecutive vertices.

Sum of the Measures of the Interior Angles of a Polygon Formula

(n-2)(180)

Sum of the Measures of the Exterior Angles of a Polygon Formula

360

Number of Diagonals Formula

n(n-3)/2

What is a regular polygon?

A convex polygon that is both equilateral and equiangular.

What is the apothem of a regular polygon?

The distance from the center of a regular polygon to each of its sides.

What is the radius of a regular polygon?

The distance from the center of a regular polygon to each of its vertices.

How do you find the area of a regular polygon?

A = 1/2 * a * P, where a is the apothem and P is the perimeter.

What is circumference?

The perimeter of a circle, calculated as C = 2πr or C = πd.

How is the area of a circle calculated?

A = πr^2

What is an annulus?

The region bounded by two concentric circles.

How do you calculate the area of an annulus?

Subtract the area of the smaller circle from the area of the larger one: πR^2 - πr^2.

What is arc length?

The distance from one endpoint of an arc to the other endpoint along the circle.

Arc Length Formula

L = (x/360) * 2πr, where x is the degree measure of the arc.

Sector Area Formula

A = (x/360) * πr^2, where x is the degree measure of the intercepted arc.

What is a segment of a circle?

A region bounded by a chord and its corresponding arc.

How do you calculate the area of a segment of a circle?

Area of Segment = Area of Sector - Area of Triangle

How do you maximize the area of a rectangle with a fixed perimeter?

The maximum area occurs when the rectangle is a square.

How do you find the vertex of a parabola?

The vertex of a parabola is the point (h, k), where h = -b/2a.

What is geometric probability?

Probability problems involving geometric ideas such as area.

Formula for Probability of an Event

P(event) = (Number of Favorable Outcomes) / (Total Number of Outcomes)