Fill in the number of sides

Polygon Name Number of Sides

Triangle

Heptagon

Nonagon

Hexagon

Pentagon

Dodecagon

Quadrilateral

Decagon

Octagon

33

7799

66

551212

441010

88

Find the Find the sum of the sum of the

measures of measures of the interior the interior angles of a angles of a Nonagon.Nonagon.

(9 – 2)180 = (9 – 2)180 =

7(180) = 7(180) =

1,2601,26000

03/12/08

Ch. 7-6 Areas of Polygons

Area is the number of square units the figure encloses.

It is flat – 2 dimensional – cm2

Example: If you were ordering carpet for a rectangular room, you would need to know the area of the room.

Important Formulas for finding area:

Parallelogram: A = bh where b is the base and h is the height

Triangle: A = 1/2bh where b is the base and h is the height

Trapezoid: A = 1/2h(b1 + b2)

Example 1: Find the area of each figures below. Use the appropriate formula.

3 cm.

7 cm.

6 cm. Area of a Triangle = ½ bh

The base is 7 and the height is 3.

A = ½ (7)(3) = 10.5 cm.2

12 cm.

20 cm.22 cm.

Area of a Parallelogram = bh

The base is 12 and the height is 20.

A = (12)(20) = 240 cm.2

Example 2: Find the area of each figure below. Use the appropriate formula.

3 m.

4 m.

6 m. Area of a Trapezoid = ½h(b1 + b2)

The bases are 6 and 3 and the height is 4.

A = ½ (4)(3 + 6) = 18 m.2

Example 3: Use the area formulas to solve for each unknown below.

a.) The area of a parallelogram is 221 yd.2 Its height is 13 yd. What is the length of its corresponding base?

Use the Area formula for a parallelogram, plug in what you know and solve for the unknown.

221 = 13b Divide both sides by 13

b = 17 yd.

b.) A triangle has area 85 cm.2 Its base is 5 cm. What is its height?

Use the Area formula for a triangle, plug in what you know and solve for the unknown.

85 = ½(5)h Multiply 5 * 1/2

85 = 5/2h Divide by 5/2, since it is a fraction you are really multiplying by the reciprocal!

2/5 * 85 = 5/2h x 2/5

34 cm. = h

Ch. 7-7 Circumference and Area of a Circle

Important formulas when dealing with circles:

Circumference = diameter multiplied by pi or 3.14

C =

Circumference = 2 multiplied by the radius multiplied by pi or 3.14

C =

Area of a Circle = pi multiplied by the radius squared

A =

d

r2

2r

Parts of a Circle:

Diameter

Radius

Chord

Circumference

Example 1: Find the circumference and area of each object below. Use the formulas given.

45 cm.

Find the circumference and area of the basketball hoop

C = 45 * 3.14 = 141.3 cm.

A = 3.14 * (22.5)2 = 1589.6 cm.2

Find the circumference and area of the tire

C = 12 * 3.14 = 37.68 in.

A = 3.14 * (6)2 = 113.04 in.2

12 in.

Example 2: Find the area of each irregular figure below. You are going to have to use multiple area formulas.

10 in.

7 in.

First find the area of the rectangle.

A = length multiplied by width

Area of the rectangle = 7 * 10 = 70 in. 2

Next find the area of the semi-circle

A = 2

2

1r

Area of Semi-Circle = ½ (3.14)(5)2 = 39.25 in.2

Last, add the two areas together: 39.25 + 70 = 109.25 in.2

Example 3: Find the area of each irregular figure below. You are going to have to use multiple area formulas.

19.8 m.

13.2 m.6.6 m.

First find the area of the rectangle.

A = length multiplied by width

Area of the rectangle = 19.8 * 13.2 = 261.36 m. 2

Next find the area of the semi-circle

A = 2

2

1r Area of Semi-Circle = ½ (3.14)(6.6)2 = 68.39 m.2

Last need to subtract the area of the semi-circle from the area of the rectangle

261.36 – 68.39 = 192.97 m.2

HW – Pg. 331

• PG 331 #1-4 all, 6-10 even

• PG 338 #4-22 even