Question

Two similar polygons have a scale factor of three. The smaller polygon has an area of 42 cm² and perimeter of 50 cm. what is the area of the larger polygon? and what is the perimeter of the larger polygon?

Answer 1

Explanation:

a scale factor applies to every line, that means also to every side of the polygon.

the area of a polygon is always created out of the product (multiplication) of 2 dimensions (or sides).

while a perimeter is a pure sum of sides.

so the perimeter grows by the same factor as the sides : scale factor 3.

the perimeter of the larger polygon is therefore :

50 × 3 = 150 cm

and the area of the larger polygon ?

remember, that the area is always the product of 2 sides (or the sum of products of 2 sides).

and so, the scale factor enters these multiplications twice, and it gets therefore squared : 3×3 = 9.

so, the area of the larger polygon is then

42 × 9 = 378 cm²