The problem should tell you that the shapes are similar, or it might show you that the angles are the same, and otherwise indicate that the side lengths are proportional, to scale, or that they correspond to each other.
For example, you might have a triangle with a base that is 15 cm long, and a similar triangle with a base that is 10 cm long.
For example if you are scaling down from a triangle with a 15 cm base to one with a 10 cm base, you would use the ratio Scale Factor=smallerlengthlargerlength{\displaystyle {\text{Scale Factor}}={\frac {smallerlength}{largerlength}}}. Filling in the appropriate values, it becomes Scale Factor=1015{\displaystyle {\text{Scale Factor}}={\frac {10}{15}}}.
For example, the ratio 1015{\displaystyle {\frac {10}{15}}} simplifies to 23{\displaystyle {\frac {2}{3}}}. So the scale factor of two triangles, one with a base of 15 cm and one with a base of 10 cm, is 23{\displaystyle {\frac {2}{3}}}.
For example, you might have a right triangle with sides measuring 4 cm and 3 cm, and a hypotenuse 5 cm long.
For example, if the scale factor is 2, then you are scaling up, and a similar figure will be larger than the one you have.
For example, if the hypotenuse of a right triangle is 5 cm long, and the scale factor is 2, to find the hypotenuse of the similar triangle, you would calculate 5×2=10{\displaystyle 5\times 2=10}. So the similar triangle has a hypotenuse that is 10 cm long.
For example, if the base of a right triangle is 3 cm long, with a scale factor of 2, you would calculate 3×2=6{\displaystyle 3\times 2=6} to find the base of the similar triangle. If the height of a right triangle is 4 cm long, with a scale factor of 2 you would calculate 4×2=8{\displaystyle 4\times 2=8} to find the height of the similar triangle.
Create a ratio comparing the two heights. Scaling up, the ratio is Scale Factor=546{\displaystyle {\text{Scale Factor}}={\frac {54}{6}}}. Scaling down, the ratio is Scale Factor=654{\displaystyle {\text{Scale Factor}}={\frac {6}{54}}}. Simplify the ratio. The ratio 546{\displaystyle {\frac {54}{6}}} simplifies to 91=9{\displaystyle {\frac {9}{1}}=9}. The ratio 654{\displaystyle {\frac {6}{54}}} simplifies to 19{\displaystyle {\frac {1}{9}}}. So the two rectangles have a scale factor of 9{\displaystyle 9} or 19{\displaystyle {\frac {1}{9}}}.
Irregular figures can be similar if all of their sides are in proportion. Thus, you can calculate a scale factor using any dimension you are given. [10] X Research source Since you know the width of each polygon, you can set up a ratio comparing them. Scaling up, the ratio is Scale Factor=148{\displaystyle {\text{Scale Factor}}={\frac {14}{8}}}. Scaling down, the ratio is Scale Factor=814{\displaystyle {\text{Scale Factor}}={\frac {8}{14}}}. Simplify the ratio. The ratio 148{\displaystyle {\frac {14}{8}}} simplifies to 74=134=1. 75{\displaystyle {\frac {7}{4}}=1{\frac {3}{4}}=1. 75}. The ratio 814{\displaystyle {\frac {8}{14}}} simplifies to 47{\displaystyle {\frac {4}{7}}}. So the two irregular polygons have a scale factor of 1. 75{\displaystyle 1. 75} or 47{\displaystyle {\frac {4}{7}}}.
Multiply the height of Rectangle ABCD by the scale factor. This will give you the height of Rectangle EFGH: 3×2. 5=7. 5{\displaystyle 3\times 2. 5=7. 5}. Multiply the width of Rectangle ABCD by the scale factor. This will give you the width of Rectangle EFGH: 8×2. 5=20{\displaystyle 8\times 2. 5=20}. Multiply the height and width of Rectangle EFGH to find the area: 7. 5×20=150{\displaystyle 7. 5\times 20=150}. So, the area of Rectangle EFGH is 150 square centimeters.
For example, you might need to find the molar mass of an H2O compound with a molar mass of 54. 05 g/mol. The molar mass of H2O is 18. 0152 g/mol. Find the scaling factor by dividing the molar mass of the compound by the molar mass of the empirical formula: Scaling factor = 54. 05 / 18. 0152 = 3
For example, to find the molecular formula of the compound in question, multiply the subscripts of H20 by the scaling factor of 3. H2O * 3 = H6O3
For example, the scaling factor for the compound is 3. The molecular formula of the compound is H6O3.
