Area of Quadrilateral inside a rectangle

In summary, the formula for finding the area of a quadrilateral inside a rectangle is to first find the area of the rectangle and then subtract the area of the triangle formed by the two diagonals. The area of a quadrilateral inside a rectangle can never be negative and the length of the diagonal can be found using the Pythagorean theorem. The area of a quadrilateral is always smaller than the area of the rectangle, but can be equal if the quadrilateral is a rectangle itself.
  • #1
songoku
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Homework Statement
Please see the picture below.

If AF = FB, BE = 4CE and the area of AGD = 100, find the area of CDGE
Relevant Equations
Not sure
1673404002767.png


I try to divide the area of CDGE into two areas of triangles by drawing line DE.

The ratio of area of triangles ABE and ECD = 4 : 1

The ratio of area of triangles ADG and DGE = AG : GE

The ratio of triangles ADG and AGF = DG : GF

Then I don't know what to do.
 
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  • #2
Why don't you extend AE and DC and observe they cross ,say, at H ?
 
Last edited:
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  • #3
anuttarasammyak said:
Why don't you extend AE and DC and observe they cross ,say, at H ?
I understand your hint. Thank you very much anuttarasammyak
 

1. What is the formula for finding the area of a quadrilateral inside a rectangle?

The formula for finding the area of a quadrilateral inside a rectangle is the length of the rectangle multiplied by the height of the quadrilateral.

2. Can the area of a quadrilateral inside a rectangle ever be greater than the area of the rectangle itself?

No, the area of a quadrilateral inside a rectangle can never be greater than the area of the rectangle itself. This is because the quadrilateral is always a smaller shape within the larger rectangle.

3. How do you find the length and height of a quadrilateral inside a rectangle?

The length and height of a quadrilateral inside a rectangle can be found by measuring the sides of the rectangle and the diagonal of the quadrilateral. The diagonal of the quadrilateral will be the hypotenuse of a right triangle formed by the sides of the rectangle and the height of the quadrilateral.

4. Can the area of a quadrilateral inside a rectangle be negative?

No, the area of a quadrilateral inside a rectangle cannot be negative. Area is a measure of space and cannot have a negative value. If the calculation results in a negative number, it means that the quadrilateral is not fully contained within the rectangle.

5. Is the area of a quadrilateral inside a rectangle affected by the position of the quadrilateral within the rectangle?

Yes, the area of a quadrilateral inside a rectangle is affected by the position of the quadrilateral within the rectangle. If the quadrilateral is closer to one side of the rectangle, the area will be smaller than if it were closer to the opposite side.

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