Area of a Parallelogram Area of a Triangle and Area of a Parallelogram

Polygons Today we are going to find the Area of Parallelograms and the Area of Triangles

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

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

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

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

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

What is the area of the rectangle? Area of a Rectangle What is the area of the rectangle? 2 2 in. x 6 12 in.2 6 in. 12 in2 or square inches

A= s2 s Area of a Square 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. A= s2 s height = s s base = s

What is the area of the square? Area of a Square What is the area of the square? 4 4 m. 4 x 16 m.2 4 m. 16 m2 or square meters

Watch carefully not to miss it! Area of a Parallelogram 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!

Area of a Parallelogram 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

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

Check to see if you got it right. Area of a Parallelogram 2 cm. 90º 4 cm. = 8 cm.2 Check to see if you got it right.

Cut off the piece at the dotted line. Area of a Parallelogram 2 cm. 90º 4 cm. = 8 cm.2 Cut off the piece at the dotted line.

Cut off the piece at the dotted line. Area of a Parallelogram 2 cm. 90º 4 cm. = 8 cm.2 Cut off the piece at the dotted line.

Move this piece to the other side. Area of a Parallelogram 2 cm. 90º 4 cm. = 8 cm.2 Move this piece to the other side.

Move this piece to the other side. Area of a Parallelogram 2 cm. 90º 4 cm. = 8 cm.2 Move this piece to the other side.

Let’s check it with the area of a rectangle. Area of a Parallelogram Let’s check it with the area of a rectangle. 2 cm. 90º 4 cm. = 8 cm.2 Now you have a rectangle How many squares do you see? A = 8 square cm. or 8 cm.2

What is the area of this parallelogram? Area of a Parallelogram What is the area of this parallelogram? 5 5 cm. x 7 35 cm.2 7 cm. 35 square centimeters or 35 cm.2

What is the area of this parallelogram? Area of a Parallelogram What is the area of this parallelogram? 5 x 6 5 ft. 30 ft.2 6 ft. 30 square feet or 30 ft.2

Watch carefully not to miss it! Area of a Triangle 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!

Area of a Triangle Given a right triangle Make a similar triangle,

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

We can use the formula for area of a rectangle 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. height h base b What is the formula for the area of a triangle?

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

Given an isosceles triangle Area of a Triangle Given an isosceles triangle Make a similar triangle,

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

How do you find the area of the parallelogram? Area of a Triangle How do you find the area of the parallelogram? height h base

Area of a Triangle 5 cm 6 cm 3 cm 9 cm

Take out your study guide! Area of a Triangle The End! Take out your study guide!

Area of a Parallelogram # 3 To find the area for a parallelogram use what you know about area of a rectangle. A = base x height 3 in A = b x h 5 in A = 5 x 3 = 15 in2

Area of a Triangle # 4 A = base x height A = 8 x 6 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 m2 2