copyrightamberpasillas 2010 Today we are going to find
copyright©amberpasillas 2010
Today we are going to find the Area of Parallelograms and the Area of Triangles copyright©amberpasillas 2010
Area The number of square units that are needed to cover the surface of a figure. Polygon Any straight-sided closed plane figure. copyright©amberpasillas 2010
Regular Polygons Picture # of sides Name 3 Triangle Acute Equilateral 4 Quadrilateral Square 5 Pentagon Regular Pentagon 6 Hexagon Regular Hexagon copyright©amberpasillas 2010
Regular Polygons # of sides 7 Name Picture Name Heptagon 8 Octagon 9 Nonagon 10 Picture Regular Octagon Regular Decagon copyright©amberpasillas 2010
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 s s base = s copyright©amberpasillas 2010 A= s 2
What is the area of the square? 4 x 4 2 16 m. 4 m. 2 16 m or square meters copyright©amberpasillas 2010
The area of a rectangle is equal to the base times the height. Also known as length times width. height A = bh (h) base A = bh (b) is the same as copyright©amberpasillas 2010 A = lw
What is the area of the rectangle? 2 in. 6 in. 2 2 x 6 2 12 in or square inches copyright©amberpasillas 2010
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! copyright©amberpasillas 2010
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 copyright©amberpasillas 2010
Use this information to find the area of a parallelogram height = h h h b base = b A parallelogram has the same area as a rectangle! What is the formula for area of a parallelogram? copyright©amberpasillas 2010
2 cm. 90º = 8 cm. 2 4 cm. Check to see if you got it right. copyright©amberpasillas 2010
2 cm. 90º = 8 cm. 2 4 cm. Cut off the piece at the dotted line. copyright©amberpasillas 2010
2 cm. 90º = 8 cm. 2 4 cm. Cut off the piece at the dotted line. copyright©amberpasillas 2010
2 cm. 90º = 8 cm. 2 4 cm. Move this piece to the other side. copyright©amberpasillas 2010
2 cm. 90º = 8 cm. 2 4 cm. Move this piece to the other side. copyright©amberpasillas 2010
Let’s check it with the area of a rectangle. 2 cm. 90º = 8 cm. 2 4 cm. Now you have a rectangle How many squares do you see? 2 A = 8 square cm. or 8 cm. copyright©amberpasillas 2010
What is the area of this parallelogram? 5 x 7 2 35 cm. 7 cm. 35 square centimeters or 35 cm. copyright©amberpasillas 2010 2
What is the area of this parallelogram? 5 x 6 2 30 ft. 5 ft. 6 ft. 30 square feet or 30 ft. copyright©amberpasillas 2010 2
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! copyright©amberpasillas 2010
Given a right triangle Make a similar triangle, copyright©amberpasillas 2010
Given a right triangle What polygon is this? A Rectangle Make a similar triangle, flip it and put both triangles next to each other copyright©amberpasillas 2010
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. height h base b What is the formula for the area of a triangle? copyright©amberpasillas 2010
When we put 2 right triangles together is made a rectangle. Watch what happens when instead we use 2 isosceles triangles. copyright©amberpasillas 2010
Given an isosceles triangle Make a similar triangle, copyright©amberpasillas 2010
Given an isosceles triangle What polygon is this? A Parallelogram Make a similar triangle, flip it and put both triangles next to each other copyright©amberpasillas 2010
How do you find the area of the parallelogram? height h base copyright©amberpasillas 2010
5 cm 6 cm 3 cm 9 cm copyright©amberpasillas 2010
The End! Take out your study guide! copyright©amberpasillas 2010
#3 Area of a Parallelogram To find the area for a parallelogram use what you know about area of a rectangle. A = base x height 3 in 5 in A=bxh 2 = 15 in A=5 x 3 copyright©amberpasillas 2010
#4 Area of a Triangle 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. A = base x height 2 6 m 8 m A = 8 x 6 = 24 2 copyright©amberpasillas 2010 2 m
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