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# Lesson 15 — Activity 2: Estimating and Calculating the Area of Quadrilaterals

# Lesson 15 — Activity 2: Estimating and Calculating the Area of Quadrilaterals

#### Getting Ready

####
You may have learned in previous courses about polygons. A polygon is any closed two-dimensional shape that has three or more straight sides. A triangle has three sides, so it is a polygon. A rectangle has 4 sides, so it is a polygon too.

There are also four-sided shapes other than a rectangle that are polygons. These shapes are called quadrilaterals. In this activity, you will learn how to calculate the area of two quadrilaterals: squares and parallelograms.

#### Estimating the Area of Squares and Parallelograms

#### A square is a four-sided shape where all the sides are the same length. Each corner is a right angle.

#### The area of a square can be estimated using a variety of methods. One method is to use dot paper.

#### Units of measurement are called square units. Four dots make a square.

####
Square units can also be represented by units^{2}, where the 2 is an exponent.

####
unit × unit = units^{2}

Count the number of squares that can be made inside the shape.

^{2}

#### A parallelogram is a two-dimensional shape with four line segments, or sides, with opposite pairs of sides parallel and equal in length.

#### The area of a parallelogram can be estimated using a variety of methods. One method is to use grid paper.

####
Count the number of
whole squares inside the shape. The example above has 8 whole squares.
Combine partial squares to make whole squares. This example has 8
partial squares that combine to make 4 whole squares. The total area is 12 units^{2}.

#### Prove it! Use a geoboard and construct the parallelogram from the example above. Count the whole squares and combine the partial squares. (You can use a geoboard from your classroom or use the virtual geoboard by clicking here.)

#### Try This:

#### Estimate the area of the parallelogram labeled D below. You can prove your answer by using the geoboard once again. Remember to first count the whole squares and then combine the partial squares.

####
16 whole squares = 16 units^{2}

__8 partial squares = 4 units__^{2}

Total area = 20 units^{2}

^{2}

http://illuminations.nctm.org

####
Calculating the Area of Squares and Parallelograms

####
To calculate the area of a square, use this formula: a^{2}

#### Using this square

#### as an example, the formula would look like this:

####
A = a^{2}

A = 7 x 7

A = 49 m^{2}^{}

^{2}

A = 7 x 7

A = 49 m

^{2}

####
To calculate the area of a parallelogram, you must do something different from squares because the shape sits at an angle. For parallelograms, you calculate area by using the height of the shape (*h*) and the length of its base (*b*).

#### Using this parallelogram

#### as an example, the formula would look like this:

A = *b* x *h*

A = 54 x 10

A = 540 km^{2}