Area PowerPoint

Report
Warm-Up
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1. Create a vocabulary and formulas flipbook!
2. Use the papers on your desk and the example on the
board to make a flipbook with 6 pages.
3. The tabs should be labeled as follows
1.
2.
3.
4.
5.
6.
Area
What is Area?
Square/Rectangle
All Triangles
Parallelogram/Trapezoid
Irregular Figures
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How do we find the area of different shapes?
Standard and Essential Question
 MCC6.G.1: Find the area of right triangles, other
triangles, special quadrilaterals, and polygons by
composing into rectangles and decomposing into
triangles and other shapes; apply these techniques in
the context of solving real-world and mathematical
problems.
How do I find the area of a square and rectangle
without a formula and decompose those to find the
area of a triangle?
What do you already know about
area? (Brainstorm)
What are the important terms?
 Area: the number of square units it takes to
completely fill a shape or surface.
 Polygon: a two dimensional (2-D) figure made up of
line segments that are connected to form a closed
shape.
 Quadrilateral: a four sided polygon
 Vertex: the end point of two or more line segments
Unit Squares
 You can count unit squares to find the area of a figure.
Height (h)
(width)
Base (b)
(length)
Area= 9 square units
Base= 3 units
Height= 3 units
Area= 4.5 square units
Base= 3 units
Height= 3 units
Geoboard Squares
 Square: a quadrilateral that has 4 congruent sides and 4
right angles (90˚).
 Create a square that is 9 units long by 9 units wide.
 Copy that onto your dot paper!
 How many unit squares make up this quadrilateral?
 What is the area of the square?
 What is a “shortcut”/formula to find the area?
 Now put a diagonal to divide the square in half.
 When you divide the square in half what two
shapes do you get?
 What is the area of one of those shapes?
Area= 12 square units
Base= 4 units
Height= 3 units
Area= 6 square units
Base= 4 units
Height= 3 units
Geoboard Rectangles
 Rectangle: a 4-sided polygon with 4 angles that measure
90˚.
 Make a rectangle that is 8 units long and 7 units wide.
 Copy onto your dot paper!
 How many unit squares make up this shape?
 What is the area of the figure?
 What is a “shortcut”/formula to find the area?
 Now put a diagonal to divide the rectangle in half.
 When you divide the rectangle in half what two shapes
do you get?
 What is the area of one of those shapes?
So what’s the formula?
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Stacy is planting a square garden in his backyard and
needs to know how much soil to buy. One bag of soil
covers 9 ft2.
If the height of the garden is 14 ft., what is the area of the
garden?
How many bags of soil does he need?
Standard and Essential Question
 MCC6.G.1: Find the area of right triangles, other
triangles, special quadrilaterals, and polygons by
composing into rectangles and decomposing into
triangles and other shapes; apply these techniques in
the context of solving real-world and mathematical
problems.
How are areas of geometric figures related to each
other?
What about triangles?
Area of Square/Rectangle
Area of Triangle
9 units
4.5 units
12 units
6 units
14 units
16 units
What pattern do you notice?
Types of Triangles
 By Sides:
 Isosceles: a triangle that has 2 equal sides
 Scalene: a triangle that has no equal sides
 Equilateral: a triangle that has 3 equal sides
 By Angles:
 Right: a triangle with one right angle
 Acute: a triangle with only acute angles
 Obtuse: a triangle with one obtuse angle
Other Important Terms
 Height of a triangle: The perpendicular distance
from the base to the highest vertex.
It can be
measured outside
the triangle!
It can be
measured inside
the triangle!
Does the area change depending
on the type of triangle?
 Use the link below to determine whether the area
formula of a triangle changes depending on the
type of triangle.
 http://www.geogebra.org/en/upload/files/english/Vic
toria/TriangleArea.html
How can I
determine the
area by only
counting unit
squares?
Let’s do some examples…
 What’s the area?
9.4 ft.
7 ft.
Area= 32.9 ft2
-----------------------------
 What’s the area?
6 cm.
4 cm.
Area= 12 cm2
So what are the 2 ways to find the
area of a triangle?
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1.
-----------------------------
 Find the area of the following triangles.
2.
11.7 cm.
5m
9m
6 cm.
Standard and Essential Question
 MCC6.G.1: Find the area of right triangles, other
triangles, special quadrilaterals, and polygons by
composing into rectangles and decomposing into
triangles and other shapes; apply these techniques in
the context of solving real-world and mathematical
problems.
How can we use our knowledge of the area of one
figure to determine the area of another?
---------------------------
---------------------------
Parallelogram
A quadrilateral with both pairs
of opposite sides parallel
Think about it!
Do you think you can determine how to
find the area of the parallelogram using
the shapes we’ve already discussed?
How do you get the area?
 http://learnzillion.com/l
A=bh
essons/1058-find-thearea-of-a-parallelogramby-decomposing
Height (h)
Base (b)
Let’s do some examples…
 What is the area?
-------------------
12 m
15 m
4.8 m
-------------------
 What is the area?
24 m
Area= 360 m2
Area= 57.6 m2
---------------------------
Trapezoid
---------------------------
A quadrilateral which has one
pair of parallel sides
Think about it!
Do you think you can determine how to find
the area of the trapezoid using the shapes
we’ve already discussed?
How do you get the area?
---------------------------
---------------------------
Base 2 (b2)
Base 1 (b1)
Height (h)
Let’s do some examples…
 What’s the area?
 What’s the area?
9 cm
10 cm
15 cm
Area= 60 m2
Area= 120 cm2
1 ft.
---------------------------
Daniel has a room in his house shaped like a trapezoid.
Use the picture of Daniel’s room to answer the following
questions.
7 ft.
4 ft.
8 ft.
1. What is the area of the room? 32 ft.2
2. If one tile can cover 1.5 square feet, how many tiles
does Daniel need to cover the entire room?
22 tiles
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---------------------------
---------------------------
A square poster board has sides that are 40 inches long.
When the triangular flaps at the sides are opened, the
poster board takes the shape of a trapezoid. The base of
each of the triangles is 24 inches. What is the area of the
trapezoid poster board?
Standard and Essential Question
 MCC6.G.1: Find the area of right triangles, other
triangles, special quadrilaterals, and polygons by
composing into rectangles and decomposing into
triangles and other shapes; apply these techniques in
the context of solving real-world and mathematical
problems.
How can you find the area of irregular polygons
when you don’t have a specific formula?
Irregular Shapes
So how am I supposed to
find the area for that?
Method 1: Counting Squares
Area=
18 units2
How can you count squares?
Hint!
Create two
squares
using the
triangles to
help find
the area!
Area=
16 units2
Method 2: Find the area of the whole figure
and then subtract the shapes that aren’t
included.
12 ft.
2 ft.
7 ft.
3 ft.
3 ft.
10 ft.
120
ft2
–9
ft2
12 ft.
10 ft.
Area= 111 ft2
Method 3: Find the area of the shapes
separately and add their areas together.
25 mm.
12 mm.
625 mm2
(square area)
25 mm.
+ 150 mm2
(triangle area)
Area= 775 mm2
Counting Squares Challenge
Area=
38.5 units2
Method 2 Challenge
15 ft.
6 ft.
4 ft.
4 ft.
11 ft.
2 ft.
4 ft.
4 ft.
4 ft.
Area= 235 ft2
Online Area Games
 Triangle Area Game
 http://www.shodor.org/interactivate/activities/Triangl
eExplorer/
 Area Explorer Game
 http://www.shodor.org/interactivate/activities/AreaEx
plorer/

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