∆abc is similar to ∆def. the perimeter of ∆abc is five times the perimeter of ∆def. the area of ∆abc is 100 square centimeters. the area of ∆def is square centimeters. nextreset

The area of ∆DEF is 4 square centimeters.

Step-by-step explanation:

Given ∆ABC is similar to ∆DEF.

The perimeter of ∆ABC is five times the perimeter of ∆DEF. It means:-

(perimeter of ΔABC) = 5 times (perimeter of ΔDEF)

(perimeter of ΔABC) / (perimeter of ΔDEF) = 5

It means Scale factor, K = 5.

Given The area of ∆ABC is 100 square centimeters.

(area of ∆ABC) / (area of ∆DEF) = k²

100 / (area of ∆DEF) = 5² = 25.

(area of ∆DEF) = 100 / 25 = 4.

Hence, The area of ∆DEF is 4 square centimeters.

4 square centimeters

Step-by-step explanation: