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Three math problems! Please explain the process and ideas clearly! thank you
Solution:

Connect alternating current,

As can be seen from the figure, the heights of triangle ABE and triangle ACE are equal (the height is the distance from A to BC).

S=L*H

So the area ratio = the bottom ratio.

S(ABE)/S(ACE)=BE/CE= 1/2

Similarly: S(ACF)/S(ADF)=CF/DF.

S(ABE)= 12,

Then s (ace) = 24 cm 2.

s(abc)=s(abe)+s(ace)= 12+24=36cm^2

Because ABCD is a parallelogram,

S(ABC)=S (automatic call distributor) =36

Because S(ACF)/S(ADF)=CF/DF.

DF=CF

Therefore, s (ADF) = s (ACD)/2 = 36/2 =18cm2.

Xiao Ming can be set to buy X apples!

1, ate all 5/9, missing 3: 5/9x-3.

2. After eating all 5/9, 3 are missing, and the remaining number is: x-(5/9x-3).

3. Mom brought home 3 1 apple, plus the number left before: 3 1+x-(5/9x-3).

★ Because 3 1 apple brought back by my mother is 20% more than the original, the number of apples now can be expressed as: (1+20%) x.

The above two algebraic expressions are: eating all 5/9, the total number of apples after losing 3 apples plus 3 1 apple brought back by my mother.

☆ So these two algebraic expressions are equal, and the countable equation is:

Solution: Suppose Xiaoming bought X apples.

3 1+X-(5/9X-3)=( 1+20%)X

3 1+4/9X+3= 120%X

120%X-4/9X=3+3 1

34/45X=34

X=45

A: Xiaoming originally bought 45 apples.