Transcript 11.1 Understanding Area

11.1 Understanding Area
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.
T99: 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.
L
B
A
F
C
E
D
M
Q
N
P
O
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.
13m
3m
3m
8m
3m
3m
Method 1
1. Divide the shape into 3 rectangles.
2. Find the area of each rectangle.
3. Add the areas together.
13m
3m
3m
8m
3m
3m
A = bh + bh + bh
= 3(8) + 14(13) + 3(8)
= 24 + 182 + 24
= 230m2
13m
3m
3m
8m
3m
3m
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.
13m
3m
3m
8m
3m
3m
A = bh-4s2
= 19(14) - 4(3)2
= 266 - 36
= 230m2
40ft
30ft
38ft
35ft
Find the area of the
walkway around the pool.
Area of the whole: A = bh
= 40(35)
= 1400 ft2
Area of the Pool :
A = bh
= 30(38)
= 1140 ft2
Area of the walkway: 1400 ft2 – 1140 ft2 = 260 ft2
Assignment:
Make your own area problem! Come up with
something creative that involves several
different shapes. Write a rough draft and
then a final draft on the construction paper.
You have 15 minutes to come up with the
problem
When finished: Pass your problem to the
person behind you to calculate the area!