chapter 11 notes  Areas of Polygons and Circles

Section 11.1  Areas of Parallelograms

Area of a Parallelogram

A (area) = b (base) * h (height)    A = bh

Perimeter of any Polygon

The sum of all sides of the polygon (the distance around the polygon)

P = (add all sides)

Examples: Find the shaded area of the figure Section 11.2 Areas of Triangles, Trapezoids, and Rhombi

Area of a Triangle

A (area) = 1/2 * b (base) * h (height)

A = 1/2 bh   or  A = bh/2

Area of a Trapezoid

A (area) = 1/2 * h (height)* (b1 + b2

A = 1/2 h (b1 + b2)

Area of a Rhombus, Kite, Square
(Or ANY Quadrilateral with perpendicular diagonals)

A  = 1/2 * d1 * d2        d1 and d2 are the diagonals

Postulate 11.1:  Congruent figures have equal areas

Examples: Section 11.3 Areas of Regular Polygons and Circles

Regular Polygon:  a polygon with congruent sides and congruent angles

Parts of a Regular Polygon

Center of a Regular Polygon—the center of the circumscribed circle.

Radius of a Regular Polygon—the radius of the circumscribed circle.

Apothem of a Regular Polygon—the distance from the center to the midpoint of any side of the polygon.

Central Angle of a Regular Polygon—an angle whose vertex is the center and whose sides contain two consecutive vertices of the polygon. Area = 1/2 * Perimeter * apothem

To find the area of a Regular Polygon:

Find each of the following values:

Apothem (a)

Base (b)

Side (s)

Perimeter (P)

Area (A)   Area of a Circle Examples: Section 11.4 Areas of Irregular Figures

Examples of Irregular Polygons: Section 11.5 Geometric Probability

Sector:  portion of a circle bounded by a central angle and its intercepted arc Area of a Sector N is the measure of the central angle (or the intercepted arc)
r is the radius of the circle

Probability:  desired outcome (area)/ possible outcome (area)

The probability of an event = successful possible area / total possible area

OR

The probability of an event = successful possible length / total possible length      