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copyright©amberpasillas2010

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Today we are going to find the Area of Parallelograms a nd the Area of Triangles

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Area The number of square units that are needed to cover the surface of a figure. Polygon Any straight-sided closed plane figure.

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copyright©amberpasillas2010 Circle the polygons below. Regular Polygon Polygon with all sides congruent and all angles congruent.

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Polygons Regular Polygons Name # of sides Picture Name Picture 3 Triangle Acute Equilateral 4 Quadrilateral Square 5 Pentagon Regular Pentagon 6 Hexagon Regular Hexagon

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copyright©amberpasillas2010 Polygons Regular Polygons Name # of sides Picture Name Picture 8 Octagon Regular Octagon 10 Decagon Regular Decagon 7 Heptagon 9 Nonagon

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copyright©amberpasillas2010 The area of a rectangle is equal to the base times the height. Also known as length times width. height base (h) (b) A = bh A = bh is the same as A = lw

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copyright©amberpasillas2010 What is the area of the rectangle ? 2 in. 6 in. 2 6x 12in in 2 or square inches

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copyright©amberpasillas2010 A square is a special rectangle. Since the base and the height are the same size, we call them sides ( s ) instead of base and height. s height = s s base = s A= s 2

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copyright©amberpasillas2010 What is the area of the square ? 4 m. 4 4 x 16m m 2 or square meters

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copyright©amberpasillas2010 Given the formula for area of a rectangle, we are going to use that information to derive the formula for the area of a parallelogram Watch carefully not to miss it!

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Draw a straight line from the top corner perpendicular to the base Cut that triangle and move it to the other side What shape does it make? Rectangle

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copyright©amberpasillas2010 What is the formula for area of a parallelogram ? Use this information to find the area of a parallelogram A has the same area as a rectangle! h base = b height = h h b

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copyright©amberpasillas cm. 90º 2 cm. = 8 cm. 2 Check to see if you got it right.

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copyright©amberpasillas cm. 90º 2 cm. = 8 cm. 2 Cut off the piece at the dotted line.

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copyright©amberpasillas cm. 90º 2 cm. = 8 cm. 2 Cut off the piece at the dotted line.

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copyright©amberpasillas cm. 90º 2 cm. = 8 cm. 2 Move this piece to the other side.

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copyright©amberpasillas cm. 90º 2 cm. = 8 cm. 2 Move this piece to the other side.

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copyright©amberpasillas cm. 90º 2 cm. = 8 cm. 2 Now you have a rectangle A = 8 square cm. or 8 cm. 2 Lets check it with the area of a rectangle. How many squares do you see?

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copyright©amberpasillas2010 What is the area of this parallelogram ? 7 cm. 5 cm. 5 7 x 35cm square centimeters or 35 cm. 2

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copyright©amberpasillas2010 What is the area of this parallelogram ? 6 ft. 5 ft. 5 6 x 30ft square feet or 30 ft. 2

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copyright©amberpasillas2010 Given the formula for area of a rectangle, we are going to use that information to discover the formula for the area of a triangle. Watch carefully not to miss it!

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Given a right triangle Make a similar triangle,

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Given a right triangle Make a similar triangle, flip it and put both triangles next to each other What polygon is this? A Rectangle

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copyright©amberpasillas2010 What is the formula for the area of a triangle ? We can use the formula for area of a rectangle to find the formula for area of a triangle. Two triangles make one rectangle. We want to find half of the area of the rectangle. base height b h

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When we put 2 right triangles together is made a rectangle. Watch what happens when instead we use 2 isosceles triangles.

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Given an isosceles triangle Make a similar triangle,

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Given an isosceles triangle Make a similar triangle, flip it and put both triangles next to each other What polygon is this? A Parallelogram

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copyright©amberpasillas2010 base height h How do you find the area of the parallelogram?

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copyright©amberpasillas cm 5 cm6 cm 3 cm

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The End! Take out your study guide!

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copyright©amberpasillas2010 Area of a Parallelogram # 3 5 in 3 in A = b x h A = 5 x 3 = 15 in 2 To find the area for a parallelogram use what you know about area of a rectangle. A = base x height

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copyright©amberpasillas2010 # 4 Area of a Triangle 8 m 6 m A = 8 x 6 2 = 24 m 2 A = base x height 2 A triangle is half the area of a rectangle. To find the area of a triangle you use the rectangle formula and divide it in half.

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