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
 

FAQ: Area of Quadrilateral inside a rectangle

How do you calculate the area of a quadrilateral inside a rectangle?

To calculate the area of a quadrilateral inside a rectangle, you can use various methods depending on the type of quadrilateral. For simple shapes like rectangles and parallelograms, you can use the base times height formula. For more complex quadrilaterals, you might need to divide the shape into triangles and use Heron's formula or the Shoelace theorem.

Can a quadrilateral inside a rectangle have an area larger than the rectangle itself?

No, a quadrilateral inside a rectangle cannot have an area larger than the rectangle. The area of any shape within a rectangle is always less than or equal to the area of the rectangle.

What is the maximum area a quadrilateral can have inside a rectangle?

The maximum area a quadrilateral can have inside a rectangle is equal to the area of the rectangle itself. This occurs when the quadrilateral is the rectangle.

How do you find the area of an irregular quadrilateral inside a rectangle?

To find the area of an irregular quadrilateral inside a rectangle, you can divide the quadrilateral into two triangles. Calculate the area of each triangle using the formula 0.5 * base * height or Heron's formula, and then sum the areas of the two triangles.

Is there a specific formula for the area of a cyclic quadrilateral inside a rectangle?

Yes, for a cyclic quadrilateral (a quadrilateral inscribed in a circle), you can use Brahmagupta's formula: Area = sqrt((s-a)(s-b)(s-c)(s-d)), where a, b, c, and d are the side lengths of the quadrilateral, and s is the semiperimeter (s = (a+b+c+d)/2).

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