Question

The dark shape is the picture, and the light shape is the mat

(a) For both the picture and the mat, determine the ratios of the perimeter of the scaled image to the perimeter of the original item.

(b) For both the picture and the mat, determine the ratios of the area of the scaled image to the area of the original item.

Answer 1

Polygons are similar when their corresponding angles are equal and their corresponding sides are in the same proportion. Just as their corresponding sides are in the same proportion, perimeters and areas of similar polygons have a special relationship.

Perimeters: The ratio of the perimeters is the same as the scale factor. In fact, the ratio of any part of two similar shapes (diagonals, medians, midsegments, altitudes, etc.) is the same as the scale factor.