bellwork find the area of the shapes described: find the area of the shapes described: 1.rectangle...

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Bellwork• Find the area of the shapes

described:

1. Rectangle with sides 4 inches by 7 inches.

2. Square with side 8 yards.

3. Rectangle with sides 2 meters by 11 meters.

4. Square with side 6 feet.

5. Rectangle with sides 2 feet by 6 inches.

Answers:

1. 28 inches2

2. 64 yards2

3. 22 meters2

4. 36 feet2

5. 144 inches2 or 1

foot2

GeometryAREA: RECTANGLES, SQUARES, PARALLELOGRAMS AND TRIANGLES

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Area• Area is defined as the extent or measurement of a surface.

• This means that it is given by two dimensions (usually length and width)

• This requires then that the result be given a two dimensional notation, thus we add the superscript 2 to the units used. This denotes the units of measure (feet, inches, meters, etc) and tells the person looking at the information that it is in two dimensional space (thus the reason for the 2).

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The Area of a Rectangle

•Many of you already know how to find the area of a rectangle

• This formula is generalized by However, these two can be substituted with any two directions of a rectangular parcel, such as height or depth.

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Area of a Square

• The area of the square is much the same as that of a rectangle (since all squares are rectangles). However, since all the sides of the square are the same we can simplify the equation to becoming or .

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Area of a Parallelogram

• The area of a parallelogram is given by

• Thus for the given picture, the area would

be given by .

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Why does that work??

By making one cut from a vertex of the parallelogram perpendicularly to the opposite side, we create a triangle which can be placed on the opposite side of the parallelogram, thus turning it into a rectangle with dimensions

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So what about the area of a triangle??

• The area of a triangle with base, , and height, can be demonstrated as being one half the area of a parallelogram with the same base and height.

• Thus the area of a triangle is:

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Example 1: Find the area

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Example 2: Find the missing information

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Example 3: Find the area

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Example 4: Find the area

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Example 5: Find the missing information

HomeworkASSIGNMENT 9-1