Question

An equilateral triangle with sides 10 cm is inscribed inside a similar triangle. The larger triangle is dilated with a scale factor of 3 from the smaller triangle. Using the ratios of areas, find the area of the shaded region.

Answer 1

To solve this exercise you must follow the proccedure shown below:

 1. You have the the lengths of the sides of equilateral triangle which is inscribed inside a similar triangle are 10 cm. Therefore, the area is:

 A1=bxh/2
 A1=10 cmx10 cm/2
 A1=50 cm²

 2. The larger triangle is dilated with a scale factor of 3 from the smaller triangle. Using the ratio of the area:

 (1/3)²=50/A2
 1/9=50/A2
 A2=450 cm²

 3. The area of the shaded region is:

 At=A2-A1
 At=400 cm²