Understanding AreaLesson 11.1

Understanding AreaLesson 11.1

Units of measure

1. Linear units: perimeter, circumference

2. Square units: area

3. Cubic units: volume

Definition: The area of a closed region is the number of square units of space within the boundary of the region.

Area of a rectangle:

Arect = bh

where b is the length of the base and h is the length of the height.

Theorem 99: the area of a square is equal to the square of a side.

Asq = s2

where s is the length of a side.

Postulate: every closed region has an area.

If two closed figures are congruent, then their areas are equal.If ABCDEF is congruent to LMNOPQ, then the area of region 1 is equal to the area of region 2.

A B

C

DE

F

L M

NQ

OP

1 2

Postulate: If two closed regions intersect only along a common boundary, then the area of their union is equal to the sum of their individual areas.

= +

To solve these problems:

1. Write the correct formula

2. Plug in the correct numbers

3. Compute and give answer with correct units. (minimum 3 lines!)

4. For irregular shapes, divide it into individual shapes, solve each shape and then add together.

Example:

Find the area of the shape below.

3m

3m

3m

3m

13m

8m

1. Divide the shape into 3 rectangles.

2. Find the area of each rectangle.

3. Add the areas together.

Method 1

3m

3m

3m

3m

13m

8m

A = bh + bh + bh

= 3(8) + 14(13) + 3(8)

= 24 + 182 + 24

= 230m2

3m

3m

3m

3m

13m

8m

Method 2

1. Calculate the base and height of the original rectangle, find total area.

2. Calculate the area of the 4 corners.

3. Subtract the 4 corners from the total area.

3m

3m

3m

3m

13m

8m

A = bh-4s2

= 19(14) - 4(3)2

= 266 - 36

= 230m2

Find the area of the walkway around the pool.

40ft

35ft38ft

30ft

A = bh – bhA = 40(35) – 38(30)A = 1400 – 1140A = 260 ft2

Time to Paint the Classroom…

This classroom could use a fresh coat of paint. With your team, determine how many square feet will need to be painted.Keep your calculations secret until we reveal them to the class.