Transcript UnderstandingArea

Understanding Area
Lesson 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.
L
B
A
1
F
E
C
D
M
2
Q
P
N
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.
A = bh – bh
A = 40(35) – 38(30)
A = 1400 – 1140
A = 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.