If Figure B is similar to Figure A by a scale factor k, then the area of Figure B is the area of Figure A multiplied by the square of the scale factor.
See solution.
Practice makes perfect
We are asked to consider a situation where we know that two figures are similar and are given the areas of both figures. We want to explain how we can determine the scale factor of the similarity. Let's consider two example similar figures.
If Figure B is similar to Figure A by scale factor k, then the area of Figure B is the area of Figure A multiplied by the square of the scale factor k.
Area ofB = Area ofA * k^2
We know the areas of both figures, so let's substitute them into this equation. The area of Figure A is 16 square inches, while the area of Figure B is 64 square inches.
Area ofB = Area ofA * k^2 ⇓ 64 = 16 * k^2
Now we can solve this equation to find k. Let's do it!
The scale factor must be positive, so the value of k is 2. Therefore, Figure B is similar to Figure A by a scale factor of 2. In general, to find the scale factor by which one figure is similar to another, we divide the area of the first figure by the area of the second figure and find the square root of the quotient.
