If the perimeter of a polygon is 10, and the perimeter and area of a similar polygon are 20 and 24, respectively, then the area of this polygon is 6? Well no? Why?
Let P1 be the perimeter of the first polygon S1 – the area of the first polygon, P2 and S2 the perimeter and the area of the second polygon.
Since polygons are similar, the ratio of their perimeters is equal to the coefficient of their similarity.
P1 / P2 = 10/20 = 1/2.
The areas of such polygons are related as the square of their coefficient of similarity.
S1 / S2 = K ^ 2 = 1/4.
S1 = S2 / 2 = 24/4 = 6 cm2.
Answer: The area of the first polygon is 6 cm2.
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