Point D, E and F is set by extending three sides AB, BC, and CA of triangle ABC twice respectively as shown in the figure below.
How many times of the area of triangle ABC is the area of triangle DEF ?
How many times of the area of triangle ABC is the area of triangle DEF ?
Answer
Solution
Comparing the area of the triangle FCE and triangle ABC, base CE and BC is equal and height AC : FC = 1 : 2, assuming the area of triangle ABC is 1, the area of the triangle FCE is 2.
Both area of triangle FDA and triangle EBD will also be 2 in the same way.
Therefore, the area of the triangle DEF is 2 + 2 + 2 + 1 = 7 which is seven times of that of ABC.
Seven times
Comparing the area of the triangle FCE and triangle ABC, base CE and BC is equal and height AC : FC = 1 : 2, assuming the area of triangle ABC is 1, the area of the triangle FCE is 2.
Both area of triangle FDA and triangle EBD will also be 2 in the same way.
Therefore, the area of the triangle DEF is 2 + 2 + 2 + 1 = 7 which is seven times of that of ABC.
