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.

This image shows a parallelogram.


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.


Square Image 1

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.

This image shows a square unit.

Square units can also be represented by units2, where the 2 is an exponent. 

unit × unit = units2

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


This image shows how to estimate the area of a square.

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


This image shows a parallelogram.

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

This image shows how to estimate the area of a parallelogram.


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 units2.

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.



Parallelogram Image for Try This


16 whole squares = 16 units2
8 partial squares  =   4 units2
Total area                 = 20 units2


Image of parallelogram courtesy of © 2008 National Council of Teachers of Mathematics
http://illuminations.nctm.org


Calculating the Area of Squares and Parallelograms


To calculate the area of a square, use this formula: a2


Using this square

Square Image 1

as an example, the formula would look like this:


A = a2
A = 7 x 7
A = 49 m2


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

This image shows a parallelogram.

as an example, the formula would look like this:

A = b x h

A = 54 x 10

A = 540 km2

Images courtesy of www.imagesgoogle.com and K&E Studio 

Go to the next page to try a Self-check Activity to further practise finding the area of squares and parallelograms.