DimensionsIn this lesson, we'll take a look at what happens to the area of a figure if you increase its dimensions, for example, by doubling each.
What happens to the area of a rectangle if you double the width and double the length? Many people think that the area doubles, but that is wrong. The area quadruples--it multiplies by 4. Let's look at why this is the case. We're doubling the length, and doubling the width, but remember that these two dimensions get multiplied together. That means we are multiplying an extra 2 x 2, which means the area increases by a factor of 4. It gets quadrupled. The same would be true for a square, or parallelogram, or any figure in which we multiply length and width to find the area.
What happens if we triple each dimension? The area would be multiplied by 9. Each dimension is multiplied by the other, so we're increasing the area by 3 x 3 or 32, which is 9. The area is 9 times a great.
What happens if we multiply one dimension by 3 and the other by 2? The area would be multiplied by 3 x 2, or 6. Make sure you understand this.
What happens if we double the radius of a circle? The radius is being multiplied by 2, but as part of our formula, we are squaring that 2. This means that the area is quadrupled.
Make sure that you feel comfortable with these ideas, since test-makers love to try to trick you with these concepts. This idea also comes up in everyday life. If you are going to carpet a room that is double the dimensions of another room, you don't need twice as much carpet, you need four times as much.
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