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**Area of a Parallelogram**

Area of a Triangle and Area of a Parallelogram

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

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Polygons 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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**Circle the polygons below.**

Regular Polygon Polygon with all sides congruent and all angles congruent.

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**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

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**7 8 9 10 Polygons Polygons Regular Polygons # of sides Name Picture**

Heptagon 8 Regular Octagon Octagon 9 Nonagon 10 Regular Decagon Decagon

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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

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**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

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**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

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**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

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**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!

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**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

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**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?

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**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.

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**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.

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**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.

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**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.

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**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.

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**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

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**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

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**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

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**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!

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

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**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

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**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?

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**When we put 2 right triangles together is made a rectangle.**

Area of a Triangle When we put 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**

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

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**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

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**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

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

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**Take out your study guide!**

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

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**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

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**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

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