Areas of Areas of Parallelograms and Parallelograms and

TrapezoidsTrapezoids

Areas of Areas of Parallelograms and Parallelograms and

TrapezoidsTrapezoids

• A parallelogram has two sets of parallel lines.

17 feet

12

fee

t

13 fe

et

• The formula for area is A=bh where b is the base and h is the height.

• A=(17)(12)=204 ft2.

17 feet

12

fe

et

• To see the formula visually, cut the end triangle off a parallelogram

• Move the triangle to the other side• The resulting rectangle has the same

area as the parallelogram. • To find the area of a rectangle multiply

the base times the height.

17 feet

12

fee

t

13 fe

et

f igure 3.4

Trapezoids• Trapezoids have one set of parallel

lines and one set of lines that are not parallel.

• The parallel lines are the bases. • The height is perpendicular between

the bases. • The slant heights may be the same or

they may be different.

Trapezoids

• To see how the formula for area works, visualize two of the same trapezoids put together as shown.

• Notice a parallelogram with twice the area of the desired trapezoid.

• The area of the trapezoid is ½ the area of the parallelogram with height the same as that of the trapezoid, and a base that is the sum of the two bases of the trapezoid.

base 1 or b1

base 2 or b2

height

Circumference & Area Circumference & Area of a Circleof a Circle

Circumference & Area Circumference & Area of a Circleof a Circle

The circumference of a circle is

The distance around a circle

Hint: Circumference remember circle around

First we must define some things about a

circle.

The radius is the distance from the center of a circle to any point on a circle.

Hint: I like to define it as halfway through!

The diameter is the distance across a circle through the center.

We use Pi as the measurement to help us find the circumference of a circle.

Pi, not Pie!

HINT: Pi =3.14

Two formulas are used in finding the circumference of a circle.

Circumference = d 3.14 x 4in.

12.6in.

WHEN THE CIRCLE HAS A DIAMETER MEASUREMENT, USE THE FOLLOWING FORMULA.

4in.

Circumference = 2 r

When the radius of a circle is given, the following formula should be used.

2 x 3.14 x 5cm

31.4cm

HINT: Always round your answers to the nearest tenth.

NOW…Let’s have some fun.

Tell me what formula would be used to solve the next five

problems.

3in

C = 2 x 3.14 x r

8ft

C = 3.14 d

122mm

C = 2 x 3.14 x d

17.5 cm

C = 3.14 x d

122.5mm

C = 2 x 3.14 x r

Now that we have determined the correct formula for each, let’s work the problems.

3in

C = 2 x 3.14 x r

The answer is: 18.8in

8ft

C = 3.14 d

The answer is: 25.1ft

122mm

C = 2 x 3.14 x dThe answer is:

766.2mm

17.5 cm

C = 3.14 x d

The answer is: 55cm

122.5mm

C = 2 x 3.14 x r

The answer is: 76,930mm

Classwork & Homework• CW – pg.550 #1-16 evens &

pg.#1-15 odds• WB – pg. 84 & 85