The figure below is a combination of two right triangles.
Find the area of the shaded area.
Answer
4 cm2
Solution
The area of △ABC is 4 × 6/2 = 12cm2.
△ABE and △CDE are homothetic and since the homothetic ratio is 4 : 2 = 2 : 1, AE : EC is also 2 : 1.
The area of the shaded area can be calculated by the proportional distribution of the area of △ABC which is 12cm2 × 1/(2+1) = 4 cm2.
△ABE and △CDE are homothetic and since the homothetic ratio is 4 : 2 = 2 : 1, AE : EC is also 2 : 1.
The area of the shaded area can be calculated by the proportional distribution of the area of △ABC which is 12cm2 × 1/(2+1) = 4 cm2.
