figures 1 and 2
Congruent
Notice the exponents in these two statements.Those little tiny numbers tell the whole big story:(the ratio of the surface areas of similar figures) = (the ratio of their linear dimensions)2(the ratio of the volumes of similar solids) = (the ratio of their linear dimensions)3
Its called SIMALUR * * * * * SIMILAR
Take the triangle for instance, there are 3 types. One is the same on each side which is the equilateral. But the other 2 types are flat on 2 sides and diagonal on the other side.
Whatever the ratio of perimeters of the similar figures, the areas will be in the ratios squared. Examples: * if the figures have perimeters in a ratio of 1:2, their areas will have a ratio of 1²:2² = 1:4. * If the figures have perimeters in a ratio of 2:3, their areas will have a ratio of 2²:3² = 4:9.
The areas will be proportional to (scale)2
figures 1 and 2
I guess you mean the ratio of the areas; it depends if the 2 rectangles are "similar figures"; that is their matching sides are in the same ratio. If they are similar then the ratio of their areas is the square of the ratio of the sides.
Congruent
Notice the exponents in these two statements.Those little tiny numbers tell the whole big story:(the ratio of the surface areas of similar figures) = (the ratio of their linear dimensions)2(the ratio of the volumes of similar solids) = (the ratio of their linear dimensions)3
2 dimensional figures just have width and length, if you were to add the height dimension it would become 3 dimensional.
When the shape is the same but the form is bigger or smaller
Its called SIMALUR * * * * * SIMILAR
Take the triangle for instance, there are 3 types. One is the same on each side which is the equilateral. But the other 2 types are flat on 2 sides and diagonal on the other side.
The constant of proportionality or scale factor.
The ratios of areas are the squares of the ratio of lengths (and the ratio of volumes are cubes of the ratio of lengths). As the perimeter of the second is twice the perimeter of the first, each length of the second is twice the length of the first, and so the ratio of the lengths is 1:2 Thus the ratio of the areas is 1²:2² = 1:4. Therefore the surface area of the larger prism is four times that of the smaller prism.