Welcome to Kalkulation Korner – Where mathematicians meet.
Greetings fellow mathematicians today is April 30, 2009. I am Mr. Burns and this is episode #2 of Kalkulation Korner.
In this episode we will focus our attention on finding the area of 2 dimensional figures. Before we get going I would like to suggest you get paper and something to write with so you can do the work with me. If you need to pause the recording, please do, I will be here when you get back.
All right we should all have paper and something to write with now. If you don’t you may be sorry later. Once again we must focus on definitions first. We will first define two-dimensional figure. Remember the strategy we used in episode 1, breaking the word or definition into smaller parts, lets use it again. The first word I came across is two. That is easy enough I will be working with two some things. What are those two some things? Well if I continue reading I read dimensional. Which tells us we will be working with two dimensions. What are dimensions? Well dimensions are, simply put, measurements. The last part of the phrase, two-dimensional figure, is figure. So what is a figure? A figure, for our purposes is a shape. After all the breaking apart and questions we asked we came up with a user-friendly definition for two-dimensional figure. That definition is a shape with 2 measurements. The 2 measurements are called the base and the height. The base of a figure can be described as the part the figure rests on while the height of a figure is how tall it is. There is one more definition we need to learn before we can move on and that is area. Area is the space inside of a shape and that space is measured in square units. Now that we have the definition part done we can move on to the calculations.
To find the area of a square we multiply the base and the height. This is where the pencil and paper may come in handy. You can copy the formula from the screen or just right down A=BxH. Which stands for Area equals base time height. The formula is the same when finding the area of a rectangle. Lets do a few examples before finding the area of a triangle. You may also choose to do the examples with the paper and pencil.
The first example we will try is a square with a base of 4 in. Since all the sides of a square are equal we know the height is also 4 in. The Area Equals Base Times Height or 4 in times 4 in which equals 16 inches squared. Great job on solving the first area problem of the podcast. Lets try a few more examples before we move onto area of a triangle. Lets now try to find the area of a rectangle with a base of 10in and a height of 5in. Again remember to use the formula Area = Base times Height. The area of the rectangle is 50 inches squared. Now time for on last problem involving area of a rectangle. My office is a rectangle with a base of 10ft and a height of 13ft and I want to put in some new carpet. How many square feet of carpet do I need? If you answered 130 square feet then you may have a new profession in carpet sales.
When working with triangles we use a very similar formula. The formula for finding the area of a triangle is Base times Height divided by 2. One of the best ways to learn is to do so lets try a few examples. First we will use a triangle with a base of 10in and a height of 5in. Lets put the numbers into the formula. Area = Base times Height divided by Two. So we have 10in times 5in divided by 2. First we will do the multiplication 10in times 5in is 50 inches squared the same as it was in a previous example but now we must divided it by 2 giving us 25 inches squared. Two more examples and we will be done. Find the area of a triangle with a base of 5in and a height of 14in. This one may take you a little longer to calculate. First we multiply and then we divide to get an answer of 35 inches squared. When will you ever need to know how to find the area of a triangle in real life? I will give you one example then maybe you can come up with more. You are a sailor and your main sail needs to be replaced. It is a triangular sail. The sail has a base of 10ft and a height of 34ft. How many square feet of fabric do you need to replace the old sail? The answer is 170 square feet of material. You are now ready to be a sailor.
We focused our attention on find the area of 2-dimensional figures, specifically rectangles and triangles. In order to find the areas we needed to know two different formulas. The first one was A = B x H for area of a rectangle and the second was A = B x H divided by 2 for triangles. You can use these formulas to find the areas of other shapes as well but we will save that for another time.
I hope you enjoyed your time here at Kalkulation Korner – where mathematicians meet and I hope you come back soon to explore more mathematical concepts.
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