Struggling with word problem: "ABC is a right-angled triangle at A..."

[mathyesno]

Hello there, I am struggling to understand this word problem I received for my math homework. I find it hard to understand my teacher and they did not explain this concept to me so I am really unsure how to solve it.
Any help would be so greatly appreciated as I have scoured the internet and YouTube and have not found a similar problem such as this one. (Attached)

 

[Harry_the_cat]

Please rotate the image so it can be read.

 

[lev888]

Please rotate images and brighten them if needed before posting.

 

[Dr.Peterson]

Hello there, I am struggling to understand this word problem I received for my math homework. I find it hard to understand my teacher and they did not explain this concept to me so I am really unsure how to solve it.
Any help would be so greatly appreciated as I have scoured the internet and YouTube and have not found a similar problem such as this one. (Attached)

It may help if you construct the line through E parallel to AC. Then, perhaps, think about the area of triangle ADF.

I assume you have found the lengths of AC and AD and AE, all of which are easy and useful.

 

[lookagain]

Hello there, I am struggling to understand this word problem ...

You also posted this in at least one other math help site. You should be writing
back there and here with your feedback to our comments. Do not be passive.

 

[Bruce]

I put ABC on xy-plane with A(0,0) and B(3,0) and C(0,4)

Coordinates of E are found by symmetry (E is intersection of diagonals in 3x4 rectangle).

Calculate area of AEC

Next, I found coordinates of F as intersection of lines AE and DB. Then, x-coordinate of F is height of AFD, and AD is base of AFD

area AFD = 1/2*base*height

Subtract area AFD from area AEC

 

[Bruce]

I get shaded area is 15/14 square cm