Respuesta :
41 is the area of triangle.
What is quadrilateral with shape?
- A quadrilateral is a 4 sided closed figure. These figures are quadrilaterals: A shape with four sides.
- The shape has one set of parallel sides and does not have any right angles.
- There are 5 types of quadrilaterals – Rectangle, Square, Parallelogram, Trapezium or Trapezoid, and Rhombus.
1. Consider square ABCD. You know that
[tex]A_{ABCD} = AD^{2} = 200[/tex]
then
AB = BC = AC = AD = 10√2
2. Consider traiangle AED. F is mipoint of AE and G is midpoint of DE, then FG is midline of triangle AED. This means that
[tex]FG = \frac{AD}{2} = \frac{10\sqrt{2} }{2} = 5\sqrt{2}[/tex]
3. Consider trapezoid BFGC. Its area is
[tex]A_{BFGC} = \frac{FG + BC}{2}. h[/tex] where h is the height of trapezoid and is equal to half of AB. Thus,
[tex]A_{BFGC} = \frac{FG + BC}{2} . \frac{AB}{2} = \frac{5\sqrt{2 + 10\sqrt{2} } }{2} . \frac{10\sqrt{2} }{2} = 75[/tex]
4. [tex]A_{BFGC} = A_{BFGE} + A_{EGC}[/tex]
[tex]A_{EGC} = A_{BFGC} - A_{BFGE} = 75 - 34 = 41[/tex]
5. Note that angles EGC and CGD are supplementary and
Sin ∠CGD = sin ∠ EGC
Then
[tex]A_{CGD} = \frac{1}{2} CG . CD . Sin < CGE = A_{ACG} = 41[/tex]
Learn more about quadrilateral
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