8.3 Area of Squares and Rectangles Area The amount of surface covered by a figure is its area. Area is measured in square units. –in² (inches squared)

8.3 Area of Squares and Rectangles

Area

• The amount of surface covered by a figure is its area.

• Area is measured in square units.– in² (inches squared)– ft² (square feet)

Area of a Square

• Area of a Square= side x side– (side)²– A = s²

Find the area of the square

9ft

Area of a Rectangle

• Area of a Rectangle = base x height– A = bh

Base, b

Height, h

Find the area

24 ft

16 ft

A = 54 in²

9 in

h

Find the height.

Which of the following areas are you trying to find?

Parallelogram Triangle Trapezoid

AREAS OF POLYGONS

AREA OF A PARALLELOGRAM

Welcome. Today you’re going to discover the formula for area of a parallelogram.

h

b

Click to Continue

AREA OF A PARALLELOGRAM

To do this let’s cut the left triangle and…

h

b

Click to Continue

slide it…

AREA OF A PARALLELOGRAM

h

h b

Click to Continue

slide it…

AREA OF A PARALLELOGRAM

h

h

b

slide it…

AREA OF A PARALLELOGRAM

h

h

b

slide it…

AREA OF A PARALLELOGRAM

h

hb

…thus, changing it to a rectangle.

What is the area of the rectangle?

AREA OF PARALLELOGRAM

h

b

bhA hbA bhA 2

Congratulations!!!

You Answered Correctly.

Click to continue.

AREA OF A PARALLELOGRAM

Since the area of the rectangle and parallelogram are the same, just rearranged, what is the formula for the

area of this parallelogram?

h

b

bhA hbA bhA 2

Congratulations!!!

You Answered Correctly.

Click to continue.

The next slide will take you into discovering the

area of a triangle.

Do you wish to continue?

Yes No

AREA OF A TRIANGLE

Hello. You will now be discovering the formula for area of a triangle.h

bClick to Continue

AREA OF A TRIANGLE

Let’s divide the triangle so that we divide the

height in two.

b

?

?

Click to Continue

AREA OF A TRIANGLE

Now take the top and rotate…

b

?

?

Click to Continue

Remember, we divided the height into two equal

parts.

AREA OF A TRIANGLE

rotate…

?

?

AREA OF A TRIANGLE

?

?

b

rotate…

AREA OF A TRIANGLE

?

?

b

rotate…

AREA OF A TRIANGLE

?

?

b

rotate…

AREA OF A TRIANGLE

?

?

b

rotate…

AREA OF A TRIANGLE

??

b

…until you have a parallelogram.

How would you represent the height of this parallelogram?

h2 h21h

AREA OF A TRIANGLE

??

b

b

?

?

Remember, you divided the height in two.

Click to Continue

AREA OF A TRIANGLE

?

b

What is the area of this parallelogram?

bhA hbA 21 bhA 2

Congratulations!!!

You Answered Correctly.

Click to continue.

AREA OF A TRIANGLE

The area of this triangle would be the same as the parallelogram. Therefore, the formula for the area of a triangle is… what?h

b

bhA hbA 21 bhA 2

Congratulations!!!

You Answered Correctly.

Click to continue.

The next slide will take you into discovering the

area of a trapezoid.

Do you wish to continue?

Yes No

AREA OF A TRAPEZOID

Hi. Let’s derive the formula for the area for a trapezoid.

Click to Continue

AREA OF A TRAPEZOID

Remember, there are two different bases on a trapezoid.

1b

2b

h

Click to Continue

AREA OF A TRAPEZOID

1b

2b

?

?

First divide the trapezoid horizontally so the height is divided in two.

Click to Continue

AREA OF A TRAPEZOID1b

2b

?

?

Remember, we divided the height in two. Now, rotate…

Click to Continue

AREA OF A TRAPEZOID

1b

2b

?

?

rotate…

AREA OF A TRAPEZOID

1b2b

? ?

…until, you have a parallelogram.

Click to Continue

AREA OF A TRAPEZOID

1b2b

?

How would you represent the height of the parallelogram?

h h2 h21

AREA OF A TRAPEZOID

1b

2b

?

? 1b2b

?

Remember, we divided the height in two.

Click to Continue

AREA OF A TRAPEZOID

1b2b

?

How would you represent the base of the parallelogram?

)( 12 bb ))(( 21 bb )( 12 bb

AREA OF A TRAPEZOID

1b

2b

?

? 1b2b

?

The new base is made by connecting the top and bottom bases.

Click to Continue

AREA OF A TRAPEZOID

1b2b

?

How would you represent the area of this parallelogram?

)( 321 bhA )( 212

1 bbhA 2121 bhbA

AREA OF A TRAPEZOID

It is improper to add subscripts.Try again.

Click to Continue

AREA OF A TRAPEZOID

Reminder.In order to add before

multiplying you must use grouping symbols.

Click to Continue

AREA OF A TRAPEZOID

The area of this trapezoid is the same as the parallelogram.

What is the formula for area of a trapezoid?

1b

2b

h

2121 bhbA )( 32

1 bhA )( 2121 bbhA

Congratulations!!!

You Answered Correctly.

Click to continue.

Sorry!!! Try again.

Click to continue.

AREAS OF POLYGONS

Once you have finished with the handouts and tests you will have completed the unit on areas of parallelograms, triangles, and trapezoids.

Have a good day.

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