Area of Irregular Shapes
When we first started learning about geometric shapes we worked almost solely on regular shapes. This figures all shared the same measures of the interior angles and their sides. It makes them appear uniform and for a lack of a better word, regular. There are times where these measures will not be consistent in the same shape, and it will give off an odd appearance. We call shapes that having an out of sync set of measures and length of sides irregular. Sometimes these figures get a bit out of hand and compound or stack upon themselves or other shapes. On of the beauty things about shape geometry is that often these irregular shapes are just a stack of a bunch of regular shapes. If you add the measures of all the regular shapes your sum is the measures of the irregular shape. When we are working with two dimensional figures there are many times that we will need to know the shape that it occupies, this usually requires us to determine the length of two measures, but irregular shapes complicate things a bit. These worksheets and lessons help students understand how to find indirect area of these forms and various locations using a technique that allows us to break apart irregular shapes.
Aligned Standard: Grade 6 Geometry - 6.G.A.1
- Area of a Double Rectangle Step-by-step Lesson- We give you an "L" shape and ask you to break it into two rectangles to determine the area.
- Guided Lesson - You will work on the area of two triangles and an odd rectangle series.
- Guided Lesson Explanation - I think this is a good outline to help students really understand the concept of area.
- Practice Worksheet - I add perimeter and area comparisons. I see these types of questions on a number of national exams.
- Area of Polygons and Circles Five Pack - The focus here is on more standard shapes.
- Perimeter Matching Worksheet - Sorry about that. Perimeter does fall under this standard too.
- Answer Keys - These are for all the unlocked materials above.
These are the types of problems professional contractors deal with daily.
- Homework 1 - What is the area of this triangle? As long as you account for all the measures, you are all good.
- Homework 2 - What is the area of this figure? These are common problems you will come across when working in construction.
- Homework 3 - Which figure has a greater perimeter? Remind yourself that these are all not to scale.
These are the types of problems that teachers work with daily.
- Practice 1 - A regular hexagon is a six sided polygon where each side is of equal length. This length is also equal to the radius (r) of the hexagon.
- Practice 2 - A square is a quadrilateral where all four sides are of equal length.
- Practice 3 - Find the area of some wild shapes.
Math Skill Quizzes
Students should hopefully sail through these.
- Quiz 1 - All quizzes are a mixed review in this section. You will do some comparisons and calculations.
- Quiz 2 - Which figure has a greater perimeter?
- Quiz 3 - More perimeter problems for you to tackle. I would recommend checking things off as you go.
How to Approach Finding the Area of Irregular Shapes
While there are many symmetrical shapes in geometry, you will find many asymmetrical forms too. These are called irregular shapes. Irregular shapes can have just about any number of sides, but almost always are composed of varying lengths. This results in non-traditional geometric figures being formed. At first the hardest part is to find out the area of these odd constructions. The truth is that if you look deeply into the structure of these forms, you will see that it is often composed of smaller traditional geometric shapes. When it comes to learning the dimensions of the overall shape, we need to keep in mind that if we know the dimensions of these smaller parts, the sum of all them is the dimensions of the irregular shape.
In order to learn how we can go about finding the areas of these shapes, let's look at the following steps. The first approach is to decompose these shapes into triangles, squares, quadrilaterals or any other shape to form a regular shape. To evaluate such pieces, you can divide the shapes into unit squares. The total number of unit squares that fall within the shape determines the area of the figure. If you have shaded unit squares, count squares as 1 if the shaded region is more than half the square. Divide the irregular shape into two or more regular shapes to find the area. Use curves to divide the irregular shapes into regular molds. Using these dividing techniques, you can easily find the area of odd shapes that are a part of geometry. We will put this into action in a full example problem. What is the area of this figure?
Before we begin to break this down, notice that it is an irregular shape that is composed of two rectangles (A and B). If we can find the area of each of those rectangles, it stands to reason that their sum would be the total area of the irregular shape. We also have to remind ourselves that the area of a rectangle is base times height.
Step 1) Starting with rectangle A. Rectangle A is 60 inches wide and 25 inches tall. To find the area of a rectangle we multiply base (60) times height (25). 60 × 25 = 1500. We now know that the area of rectangle A is 1500 in2.
Step 2) Now we should move to rectangle B. Rectangle B is 20 inches wide and 25 inches tall. To find the area of B we do the thing and multiply the base times height: 20 × 25 = 500. The area of rectangle B is 500 in2.
Step 3) We will add the areas of the two rectangles to find the overall area of the irregular shape. 1500 in2 + 500 in2 = 2000 in2. So, the area of this irregular shape is 2000 square inches.
Why Is This Skill Important?
Almost all forms building or construction projects involve this skill at some point. Whether it be during the initial architectural design or if a client asks them to add a closet somewhere on the blueprint. The architect can only work with the area that the original design calls for. When the construction begins they will often run into problems based on the wiring, heating, and cooling of the house. They may need to shimmy something around, once built it may not look the best, or there might be a piece of furniture or kitchen appliance that requires changes to be made. In the medical field computers and radiologists are performing similar calculations to determine the size of unknown growths in their patient’s bodies. Understanding the shape and being able to detect and track these growths are often key to staying healthy.