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## Warm-Up 1/29

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### Area!!

Warm-Up 1/29

- Create a vocabulary and formulas flipbook!
- Use the papers on your desk and the example on the board to make a flipbook with 6 pages.
- The tabs should be labeled as follows
- Area
- What is Area?
- Square/Rectangle
- All Triangles
- Parallelogram/Trapezoid
- Irregular Figures

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 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)

Geoboard Squares

- 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?

- Square: a quadrilateral that has 4 congruent sides and 4 right angles (90˚).

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?

Warm-Up 1/31

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?

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/Victoria/TriangleArea.html

Let’s do some examples…

- What’s the area?

- What’s the area?

9.4 ft.

7 cm.

6 cm.

-----------------------------

7 ft.

4 cm.

Area= 32.9 ft2

Area= 12 cm2

So what are the 2 ways to find the area of a triangle?

- Compose squares and rectangles around the triangle or decompose squares and rectangles into triangles.

- Use the formula: ½ bh

Warm-Up 2/1

- Find the area of the following triangles.

2.

1.

11.7 cm.

6.2 m

-----------------------------

5 m

9 m

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/lessons/1058-find-the-area-of-a-parallelogram-by-decomposing

A=bh

Height (h)

Base (b)

Let’s do some examples…

- What is the area?

- What is the area?

12 m

-------------------

-------------------

4.8 m

15 m

24 m

Area= 57.6 m2

Area= 360 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?

Method #1!

Get the area of both triangles and add it to the area of the rectangle.

Base 2 (b2)

Height (h)

---------------------------

---------------------------

Method #2!

Use the formula:

A= ½ h(b1+b2)

Base 1 (b1)

Daniel has a room in his house shaped like a trapezoid. Use the picture of Daniel’s room to answer the following questions.

- What is the area of the room?
- If one tile can cover 1.5 square feet, how many tiles does Daniel need to cover the entire room?

7 ft.

---------------------------

4 ft.

1 ft.

8 ft.

32 ft.2

22tiles

Warm-Up 2/4

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

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?

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.

10 ft.

12 ft.

Area= 111 ft2

120 ft2 – 9 ft2

Method 3: Find the area of the shapes separately and add their areas together.

12 mm.

25 mm.

625 mm2 (square area) + 150 mm2 (triangle area)

25 mm.

Area= 775 mm2

Online Area Games

- Triangle Area Game
- http://www.shodor.org/interactivate/activities/TriangleExplorer/
- Area Explorer Game
- http://www.shodor.org/interactivate/activities/AreaExplorer/

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