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.

Guest Jul 12, 2022

#1**+1 **

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

CPhill Jul 12, 2022