## Finding Area

11/3/2013

Finding the area can be very simple and other times it can be very difficult and frustrating. Shapes that are easy to find the area of are regular shapes. I classify regular shapes a rectangle, square, triangle, pentagon, etc...
For these shapes, you can easily put them on grid paper and count the boxes that exist within them. To get more technical, for some of these you can use an equation to find the area of these shapes such as:
Rectangle & Square: Base x Height
Triangle: 1/2 x Base x Height

Using a Geoboard I made a couple of regular shapes and found the area of them.

Finding area of a rectangle: Since I know that to find area I need to do base x height I measured with the Geoboard the side lengths. The height of the rectangle is 1 and the base of the rectangle is 4. So, 4 x 1 = 4, so the area of this rectangle is 4 units squared.

Finding area of a triangle: Now that we know the equation to find the area of a triangle is 1/2 x Base x Height I now know to measure the base and height of the triangle I made on the Geoboard. The base of this triangle is 2. The height of this triangle is 3. So now I go back to the formula, 1/2 x 2 x 3 = 3

If you wanted to count of the squares in the triangle that is possible as well, you just need to mix and match the squares that have been split. I created lines with rubber bands on the Geoboard to represent grid paper so that it would help with adding up the squares. My result of an area was still 3 units squared.

Now, I am going to get into the shapes that are more difficult to find the area of which I refer to as,irregular shapes. With irregular shapes it is more difficult to find the area by counting up the squares inside of them. So, in order to find the area of these shapes I usually split the irregular shape into different sections and work from there.

Here are some examples of irregular shapes:
I also decided to make some irregular shapes on a Geoboard and work out what the area was. I started with the shape to the left.

I decided to actually figure out the area of this shape on a piece of paper that had a Geoboard sketch on it to make things easier. I drew grid lines behind the shape to help me:

For this shape I decided to count the squares within the shape to find the area. I had to do some matching and estimating to come up with my answer. The crazy pink arrows show the pieces of square that I matched together to make 1 square unit. In the end I decided the area was approximately 5 units squared.

To the left is the second shape I created to find the area of. Once again I put this shape on Geoboard paper to make finding the area easier.

To find the area of this shape, instead of counting the squares inside the shape I decided to count the squares that were outside of the shape. Total, there are 16 squares that make up a Geoboard. When I counted the squares outside of the shape I counted that there were approximately 9 squares outside of the shape. Then I subtracted that number from 16 so, 16-9=7. From this I found that the shape had an area of approximately 7 units squared. To check, I also counted the squares on the inside. When doing this I came up with an area of 6.5 units squared. Either way I believe both methods work, but since I randomly made these shapes I'm not sure what the precise answer is. So using both of the answers I got I would say the shape had an area of around 7 units squared.

Reflection: Ever since area was introduced to me in elementary school I've always found finding the area of an irregular shape difficult. I always feel like there should be an equation for everything, but that's just how I've learned how math should be. Now doing this as a college student I find that it's okay to make mistakes and get a wrong answer. Doing these area problems it is hard to get an exact answer on your own and I feel that working together on these problems help. I also learned that there are several different ways to look at these problems and different ways to solve for the area. Everyone has different perspectives.

Feedback: What area did you receive for these shapes? What method did you use to find the area? Is there just one correct way to find area of a shape?
12/1/2013 11:17:07 pm

Many ways to find area. Formulas, partitioning, complementing (finding the outside), etc. And multiple ways within each of those.
The first odd shape is 4.5 sq units. The second is 6.5 sq units.