1. Understanding Area Lesson 11.1

2. 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.

3. 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.

4. 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. L M B A F 1 Q 2 N C D P O E

5. 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. + =

6. To solve these problems:
Write the correct formula
Plug in the correct numbers
Compute and give answer with correct units. (minimum 3 lines!)
For irregular shapes, divide it into individual shapes, solve each shape and then add together.

7. Find the area of the shape below.
Example:
Find the area of the shape below. 3m
13m 8m
Method 1
Divide the shape into 3 rectangles.
Find the area of each rectangle.
Add the areas together.

8. A = bh + bh + bh = 3(8) + 14(13) + 3(8) = 24 + 182 + 24 = 230m2 13m 3m

9. Calculate the area of the 4 corners. 3m
13m 8m
Method 2
Calculate the base and height of the original rectangle, find total area.
Calculate the area of the 4 corners.
Subtract the 4 corners from the total area.

10. 3m
13m 8m
A = bh-4s2
= 19(14) - 4(3)2 =
= 230m2

11. A = bh – bh A = 40(35) – 38(30) A = 1400 – 1140 A = 260 ft2
Find the area of the walkway around the pool.
30ft
35ft
38ft
A = bh – bh
A = 40(35) – 38(30)
A = 1400 – 1140
A = 260 ft2

12. 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.