Area!!

Warm-Up 1/29Create 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 followsArea What is Area?Square/RectangleAll TrianglesParallelogram/TrapezoidIrregular Figures

Warm-Up 1/30Area!!How do we find the area of different shapes?Standard and Essential QuestionMCC6.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 polygonVertex: the end point of two or more line segments

Unit SquaresYou can count unit squares to find the area of a figure.

Base (b)(length)Height (h)(width)

Area= 9 square unitsBase= 3 unitsHeight= 3 units

Area= 4.5 square unitsBase= 3 unitsHeight= 3 unitsGeoboard SquaresCreate 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).

Area= 12 square unitsBase= 4 unitsHeight= 3 units

Area= 6 square unitsBase= 4 unitsHeight= 3 unitsGeoboard RectanglesMake 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?

Rectangle: a 4-sided polygon with 4 angles that measure 90.

A= bhSo whats the formula?For all rectangles and squares the formula for area isWarm-Up 1/31Stacy 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 QuestionMCC6.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/RectangleArea of Triangle9 units4.5 units12 units6 units14 units16 unitsWhat pattern do you notice?Types of TrianglesBy Sides:Isosceles: a triangle that has 2 equal sidesScalene: a triangle that has no equal sidesEquilateral: a triangle that has 3 equal sidesBy Angles:Right: a triangle with one right angle Acute: a triangle with only acute anglesObtuse: a triangle with one obtuse angle Other Important TermsHeight 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 How can I determine the area by only counting unit squares?

Lets do some examplesWhats the area?Whats the area?

9.4 ft.7 ft. 4 cm.7 cm.6 cm.-----------------------------Area= 32.9 ft2Area= 12 cm2So 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: bh

Warm-Up 2/1Find the area of the following triangles.

11.7 cm.6 cm.-----------------------------9 m6.2 m5 m1.2.Standard and Essential QuestionMCC6.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

Think about it!Do you think you can determine how to find the area of the parallelogram using the shapes weve already discussed?------------------------------------------------------A quadrilateral with both pairs of opposite sides parallelHow do you get the area?http://learnzillion.com/lessons/1058-find-the-area-of-a-parallelogram-by-decomposing

Height (h)Base (b)A=bhLets do some examplesWhat is the area?What is the area?

-------------------15 m

24 m

-------------------12 m4.8 m

Area= 360 m2Area= 57.6 m2TrapezoidA quadrilateral which has one pair of parallel sidesThink about it!Do you think you can determine how to find the area of the trapezoid using the shapes weve 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)Base 1 (b1)Height (h)Method #2!Use the formula:A= h(b1+b2)Lets do some examplesWhats the area?Whats the area?

Area= 60 m2

9 cm10 cm15 cmArea= 120 cm2What 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.Daniel has a room in his house shaped like a trapezoid. Use the picture of Daniels room to answer the following questions.32 ft.222 tilesWarm-Up 2/4A 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 QuestionMCC6.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 dont have a specific formula?Irregular ShapesSo how am I supposed to find the area for that?Method 1: Counting Squares

Area= 18 units2How can you count squares?

Hint! Create two squares using the triangles to help find the area!Area=16 units2Method 2: Find the area of the whole figure and then subtract the shapes that arent included.12 ft.10 ft.10 ft.7 ft.2 ft.3 ft.3 ft.12 ft.120 ft2 9 ft2Area= 111 ft2Method 3: Find the area of the shapes separately and add their areas together.25 mm.25 mm.12 mm.Area= 775 mm2625 mm2 (square area) + 150 mm2 (triangle area)Counting Squares Challenge

Area= 38.5 units2Method 2 Challenge15 ft.4 ft.4 ft.11 ft.2 ft.4 ft.4 ft.4 ft.6 ft.Area= 235 ft2Online Area GamesTriangle Area Gamehttp://www.shodor.org/interactivate/activities/TriangleExplorer/ Area Explorer Gamehttp://www.shodor.org/interactivate/activities/AreaExplorer/