Question

Why dies multiplying 1.1 add 10% to the area?

Answer 1

Multiplying 1.1 adds 10% to the area because 1.1 is equivalent to 110% or 1 + 0.1.

To find the area of a shape, you usually multiply the length and the width. For example, the area of a rectangle with length 10 and width 5 is 10 x 5 = 50.

If you want to increase the area by 10%, you can multiply the length and the width by 1.1. For example, the new area of the rectangle with length 10 x 1.1 = 11 and width 5 x 1.1 = 5.5 is 11 x 5.5 = 60.5.

You can see that the new area is 10% more than the original area by dividing 60.5 by 50. You get 60.5 / 50 = 1.21, which means the new area is 121% of the original area, or 21% more. Subtracting 1 from 1.21 gives you 0.21, which is the same as 10%.

Another way to think about it is that multiplying by 1.1 is the same as adding 10% of the original value. For example, 10% of 10 is 1, so adding 10% to 10 is 10 + 1 = 11. Similarly, 10% of 5 is 0.5, so adding 10% to 5 is 5 + 0.5 = 5.5.

Answer 2

Remember that

100%=100/100=1

10%=10/100=0.1

so

100%+10%=110%

and

110%=110/100=1.1

so

If you multiply any area by the factor 1.1, you obtain 110% of the area

that means

you add 10% to the original area

Another example

if you multiply the area by 1.3

1.3=1+0.3

That is the same as

100%+30%=130%=130/100=1.3

you add 30% to the original area