In a figure, a quadrangle ABCD is a parallelogram.
(length of AE) : (length of ED) = 2 : 3.
The area of the triangle ABE is 80 cm2.
Find the area of triangle CDF.
Answer
75 cm2
Solution
Since the length ratio of a base of △ABE and △CED is AE : ED = 2 : 3, and height is equal, an area ratio is also set to 2 : 3.
Thus, the area of △CED =△ABE × 3/2 = 80 × 3/2 = 120cm2.
Next, △EFD and △CFB are homothetic and a homothetic ratio is ED : BC = 3 : (2+3) = 3 : 5.
Next, △EFD and △CFB are homothetic and a homothetic ratio is ED : BC = 3 : (2+3) = 3 : 5.
EF : CF is also set to 3:5.
Therefore, the area of △CDF is △CED × 5/(3+5) = 120 × 5/8 = 75cm2.
