How to Find a Side Using Area Ratios

Use a calculator when working with areas and sides of shapes.

If you are trying to teach your children about calculating area and sides of shapes -- or trying to help them with their homework -- you may come across an area ratio problem. In this type of mathematical problem, you will be given the sides of the shape in a ratio form such as 5:12 or 3:4. If you know at least one ratio measurement for a square, for example, you can calculate the area ratio and vice versa.

Instructions

1. Draw one free-form square on a piece of paper. Beside that square, write A=100.

2. Draw a second free-form square that is smaller than the first square. Beside the smaller square, write A=36. Because squares have equal sides, you know that the large square has equal sides measuring 10 (√100) and the small square has equal sides measuring 6 (√36). The formula for the area of a square is s^2 where "s" is the length of a side.

3. Calculate the sides of the square in ratio form. Because you know that the length of each side is 6 (smaller) and 10 (larger), the ratio of the sides is 6:10, which can be simplified as 3:5. The ratio of the areas of the squares is 36:100, or 9:25.

References

• Math Open Reference: Area of a Square