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Finding the Area of 2D Shapes

Depending on the shape you are finding the area of, there are actually only a few formulas that you may need to use. For example, squares, rectangles, and triangles all use the same formula (but you need to divide by 2 for a triangle!) Here, we will cover the basic rules to find the area of common shapes - and then we will try a few oddly shaped polygons!

Area of Rectangles and Squares
Finding the area of any rectangle or square, regardless of the size and dimensions is always the same. You multiple its width by its height. That's all there is to it, for all rectangles and squares!

With the shape above (not to scale!), the area is 10 * 5, which is 50. Also note that parallel sides will have the same length of sides.

Why does this work? Because the area we are dealing with is Two Dimensional (2D), meaning it has an X and Y value (X is the width, and Y is the height), the height and the width are the same regardless of where you are on the shape. So, what you are doing, is taking all of the height, and "applying" it to all of the width - creating the product (from the multiplication) that includes the width and height together. And thus, you have the area.

Area of Triangles
You have probably already noticed that any square or rectangle can be made out of two triangles. Likewise, you may have noticed that triangles are exactly one-half of a square or rectangle. Well, it is time to use that to your advantage! How? To find the area of a triangle, do the exact same steps as for rectangles and squares, and then divide by 2! Of course, the "width by height" may change a little - when using triangles, most people refer to the "width" as the "base." So the new (not really new) formula is base * height, divided by 2.

With the triangle above, we multiply height times width, just how we do with rectangles: 10 * 5 = 50. However, since a triangle is half of a rectangle, we divide by 2. Thus, 50/2 = 25, and that is the area of the triangle.

Area of Circles
Okay, you've done squares, rectangles, and triangles. Now onto circles! Unfortunately, this time there isn't just one extra step. To do this, there's a nifty little formula to use. This formula looks like this: pi * radius². So while it isn't the same as squares or rectangles, it is just as easy! All you need to do is multiple the radius by itself (square it), and then multiply it by 3.14. See these examples:

Our circle above, with a radius of 3, has an area of pi * radius². This is 3.14 * 9, which gives us a total area of 28.26.


Area of Odd and Other-Worldy Shapes
Now, what if you come across some really strange shape and you're supposed to find the area of it? Simple - just draw lines inside the shape to turn it into squares, rectangles, triangles, and circles - and solve! (Be sure to add up each individual shapes area at the end!)


That's all there is to it! Now that we've conquered 2D shapes, let's move out sights over to 3D shapes and finding their Volume. Or select another Math Topic from our Lesson Center.



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