Now we're going to look at similarity in areas of shapes. If you haven't already, go to similarity: length and make sure you know that first.
Let's start with this question:
These shapes are similar. Find the area of the smaller shape.
Ok, so first we figure out the LENGTH scale factor, like before. We know the bigger length is 5, and the smaller one is 2, so now we divide them:
5/2 = 2.5
So:
SF (length) = x2.5
One very important concept is that the scale factor for the length is NOT THE SAME as for the area. This is because the area is always in squared terms, so we SQUARE the length scale factor to get the area scale factor:
2.5 x 2.5 = 6.25
Which means:
SF (area) = x6.25
So now we divide 60cm2 by 6.25:
60/6.25 = 9.6cm2
Which means the area of the smaller shape is 9.6cm2! I will do another on volume soon. For now, why not test yourself with our quiz:
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