Honestly, I have no idea what it means by decomposition, but this is my best bet on what it means: Dividing the polygon into smaller, easier sections and solve for area and add them up.
USe the points and slope to write in y=mx+b!
x = 37.5 (or) 
Solution:
Given
.
Let us take BE = x and BC = 25 + x.
To determine the value of x:
If two triangles are similar then the corresponding angles are congruent and the corresponding sides are in proportion.


Do cross multiplication, we get


Subtract 30x from both sides of the equation.

Divide by 20 on both sides of the equation, we get
x = 37.5 (or) 
Hence the value of x is 37.5 or
.
Answer:
10 17/20 in ^2
Step-by-step explanation:
The area is
A = bh
= (7 3/4 ) * ( 1 2/5)
Changing to decimal form
7.75 * 1.4
10.85
Changing back to fraction form
10 85/100
10 17/20 in ^2