a pentagon has area 120 cm.^2 and shortest side length 8 cm. A similar pentagon has side 6 cm. What is the area of the similar pentagon?

Question

directrix · Answer

If two polygons are similar, then the square of the scale factor of the polygons is equal to the ratio of the areas of the two polygons. Assuming that 6 is the shortest side of the second polygon mentioned, then the square of 8 to 6 is equal to the ration of 120 and A where A represents the area of the second polygon.

120/A = (8/6)^2
120/A = (4/3) ^2
120 / A = 16/ 9
16 A = 120*9
A = (120 * 9 ) / 16
A = 67.5 square cm. --> Note that this answer is correct only if 6 is the shortest side of the second pentagon.