I need help with a geometry problem. S 1,2,3,4 refers to the area, nothing else is known, only that ABC is a triangle. solve for S4 (The red area)

[ptdi]

I need help with a geometry problem. S 1,2,3,4 refers to the area. Nothing else is known, only that ABC is a triangle. I need to solve for S4 (the red area).

 

[blamocur]

I haven't solved it (nor would I post the solution if I did), but I'd start by looking at ratios of segments EF/AF, DF/BF and EB/AD.

 

[Steven G]

I need help with a geometry problem. S 1,2,3,4 refers to the area. Nothing else is known, only that ABC is a triangle. I need to solve for S4 (the red area).

View attachment 37264

This is the correct place to come to for math help. Welcome!
Can you now please tell us what help you need? What have you tried? Can we see your work?
You need to understand that solving this problem for you will not be helpful.
Please try using the hints above and then show us what you have.

 

[The Highlander]

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I need help with a geometry problem. S 1,2,3,4 refers to the area. Nothing else is known, only that ABC is a triangle. I need to solve for S4 (the red area).​

View attachment 37264​

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Draw a line from from C to F thus creating two new triangles whose areas are \(\displaystyle a\) & \(\displaystyle b\) as shown above.

Let area \(\displaystyle S_4=x\).

\(\displaystyle \frac{a}{5}=\frac{x+2}{12}\\ \\and\\ \\\frac{b}{2}=\frac{x+5}{9}\)​

Formulate an equation with x as its subject and solve it to get the required area.

Hope that helps.