**estimating and justifying the area**of irregular shapes.

One tool that we have used to justify the area formulas for rectangles and right triangles has been the

**Geoboard**.

Formula for

**Rectangles**(Area = Base x Height) Formula for

**Triangles**(Area = 1/2 Base x Height)

Consider the irregular polygon shown on this Geoboard template.

**What is the area of this pentagon?**

During Math Workshop, we have approached the task of finding solutions to problems similar to this by

**decomposing**the figure into smaller

**rectangles**and

**right triangles**so that we can use the

**area formulas**for the smaller parts and then put those smaller totals together to find a justified total area.

The green rectangular area in this pentagon has a

**base**of 3 units and a

**height**of 2 units, so the area of this rectangle is 6 square units.

Area of a Rectangle = Base x Height, so 6 = 3 x 2.

(We also reference the area formula as

**length x width**.

The right scalene triangle (

**brown**) shown on the grid is exactly HALF of 2 square units (the dotted lines are shown to illustrate this idea). Therefore, the area of the triangle is 1 square unit.

Area of a Triangle = 1/2 Base x Height

The base of the triangle is 1 unit and the height of the triangle is 2 units.

(1 x 2) ÷ 2 = 1

A right scalene triangle is exactly half of a rectangle.The right isosceles triangle (

**blue**) shown on the grid is exactly HALF of 1 square unit (the dotted lines are shown to illustrate this idea). Therefore, the area of this triangle is 1/2 square unit.

Again, Area of a Triangle = 1/2 Base x Height

The base of this triangle is 1 unit and the height of the triangle is 1 unit. (1 x 1) ÷ 2 = 1/2

A right isosceles triangle is exactly half of a square.

**All decomposed parts are then combined to identify the total area of the figure**.

**The area of the pentagon is 7 1/2 square units!!**

Students, you can have fun with

**virtual Geoboards**by clicking the link below, which will take you to the Virtual Library of Math Manipulatives. (A parent may have to install Java in order for you to utilize this site.)

## Click Here: VIRTUAL GEOBOARD FUN

Also, if you would like to practice with

**transformations**, you can click the links below for some more virtual fun!

Virtual

**TRANSLATIONS**(Slides)

Virtual

**REFLECTIONS**(Flips)

Virtual

**ROTATIONS**(Turns)

**If you utilize these online resources, leave a comment to let your teachers know so you can earn some extra Behavior Bucks!**

I really understood slides, turns, etc. a lot more!

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