ABCD is a square with side length 2 cm. E is the midpoint of CD, and BF is perpendicular to AE. What is the area of ECBF, in square centimeters? Express your answer as a decimal to the nearest tenth.
+128475 F is also the midpoint of AD
Equation of line containing segment AE is
y = 2x
Equation of line containing segment BF is
y = (-1/2)x + 1
Setting these equal to get the x coordinate of the intersection of the segments
2x = (-1/2)x + 1
(5/2)x = 1
x = (2/5)
y = 2 (2/5) = 4/5
Call the intersection pt (2/5, 4/5) = G
The area of right triangle DEF = (1/2) (1) (1) =1/2
Area of right triangle AGB = (1/2)(2)(4/5) = 4/5
Area of right triangle AFG = (1/2)(2/5)(1) = 1/5
Area of ECBF =
Area of ABCD - Area of DEF - Area of AGB - Area of AFG =
2^2 - (1/2) - (4/5) - (1/5) =
4 - 1/2 - 1 =
2.5 cm^2
