Areas of Parallelograms and Trapezoids. A parallelogram has two sets of parallel lines.

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Presentation transcript:

Areas of Parallelograms and Trapezoids

A parallelogram has two sets of parallel lines.

The formula for area is A=bh where b is the base and h is the height. A=(17)(12)=204 ft2.

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.

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.

Circumference & Area of 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 d The 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