## Thursday, March 8, 2012

### Area of an Irregular Rectangular Figure

Finding Area for
An Irregular Rectangular Shape

When you first take a look at the irregular rectangular shape below, you might be unsure how to find the area for the modified shape. However, finding the area for an irregular shape like the one below takes some steps in a process, but there are two different techniques to use to help find the area. First, let's take a glance at our irregular shape below.

IMPORTANT PRECAUTIONS: When you see the irregular shape, be sure to label the missing measurements so you can go on with either of the two techniques. For the width, we know that one part of the width is 5 units, and another unlabeled width line. To find the length of this line, we must subtract 7-5. So that answer is two units. So that line is 2 units. For the length, one part of the length on the right is 3 units. So we must subtract 5-3 to find the length. So that line is 2 units long. Now, our irregular shape has all the lines labeled.  This can be done because opposite sides of a rectangle are equal.  Since this shape can fit inside a rectangle and all lines are horizontal and vertical and create right angles, you can determine missing side lengths by subtracting the known lengths.

So now that all the lines are labeled, it's time to use either of the two ways to find our area.

WAY #1:   The first way to find the area of an irregular shape is to divide it into multiple rectangles. This will make finding the area much simpler, since you will be finding the area of each divided rectangle and adding up all the areas of each of those rectangles to find the total area.

Now that the shape has been divided into smaller rectangles, let's find the area of each of the rectangles. For Shape 1: 5 X 5 = 25 units squared. For Shape 2: 2 X 3 = 6 units squared. So 25 + 6 units squared gives us our total area of 31 square units.  Be sure you are using the appropriate lengths when you are finding area.  Notice to find the area of Rectangle 1 we are multiplying 5 X 5 not 5 X 7 even though the length of the whole side is 7 units.  That length is not the length of the rectangle we broke out of our entire figure.
Now, for the second way to find the area.
WAY #2:  The other way is to make the modified shape appear as a rectangle. So, let's go ahead and make the shape into an actual rectangle.

So now, we multiply 7 X 5 to get 35 units squared for our full rectangle. After that, we will now find the area of the rectangle that was the empty space. Since we know the length and width of the rectangle, we multiply 2 X 2 to get 4 units squared. Now, we subtract the area of the full rectangle from the empty space that was made a rectangle.  35 - 4 = 31 square units, which was the answer we got from the other way to fin d the area! Using either of these processes is a matter of preference, and both will work.

JUST BE SURE TO:
• TO REMEMBER TO LABEL ALL THE LINES IN THE SHAPE BEFORE PROCEEDING WITH THESE STEPS.
• MAKE SURE YOU KNOW THE AREA OF THE DIVIDED RECTANGLE YOU ARE ADDING/SUBTRACTING.

Hope you enjoyed the article (and found it helpful) on finding the area for the irregular rectangular shape.

Post Written by: RC