If two-dimensional figures, A and B, have the same shape but each dimension of Figure B is k times the corresponding dimension of Figure A, then what is the val

Question

If two-dimensional figures, A and B, have the same shape but each dimension of Figure B is k times the corresponding dimension of Figure A, then what is the value of the ratio Area of Figure A/Area of Figure B? 

 

Area of Figure A= L*W so 1

Area of Figure B= 2L*2W so 4

Answer 1

For two similar figures with a scale factor of k:

• The ratio of their areas will be k²
• The ratio of their volumes will be k³

 

So with a scale factor of two, the ratio of the areas will be 2² = 4.  But note that k = figure B/figure A, so figure A/figure B = 1/k.  So the ratio of the area of figure A to figure B is (1/2)² = 1/4.