1. Krittika Poksawat N0.2 Class M.6/4 Tatcha Tratornpisuttikul N0.12 Class M.6/4 Worawoot Sumontra N0.23 Class M.6/4 Mahidol Wittayanusorn Constructing the quadrilateral with the maximum area when given the lengths

2. Adviser Miss Nongluck Arpasut Mr. Sunya Phumkumarn Constructing the quadrilateral with the maximum area when given the lengths

3. Introduction Currently, to find the area of any geometric figure is usually from any ready made figure. In another way, if the sides of figure are given then many geometric figures can be made. Our group will study how to construct maximal area figures especially in quadrilateral. The study is to examine that how the given four sides can be arranged and how to adjust the angles to construct a maximal area quadrilateral. Constructing the quadrilateral with the maximum area when given the lengths

5. Consider , the area of the quadrilateral Area = When given Method That is we must construct the quadrilateral in the circle. Constructing the quadrilateral with the maximum area when given the lengths

6. So that, we can find the maximum area. Area = When given Method Constructing the quadrilateral with the maximum area when given the lengths

7. Consider, the quadrilateral with the sum of the opposite angle equal to 180. Given the quadrilateral mnop with the sides, a,b,c,d . Method Constructing the quadrilateral with the maximum area when given the lengths

8. Figure 1 Figure 2 When figure 1 change to figure 2, we can suppose that the sum of the opposite angle must equal to Method Constructing the quadrilateral with the maximum area when given the lengths

9. Method 1.) Consider the order of four sides. We found that it can be 3! or 6 figures and the sum of length of three sides of quadrilateral must more than another one. Thus every quadrilaterals can construct 6 figures. 2.) Consider the order of four sides. We found that the 6 figures must have the same maximum area . The maximum area can calculate from the formula that is Constructing the quadrilateral with the maximum area when given the lengths

10. consider triangle ADC จาก law of cosine then consider triangle ABC from law of cosine then … ..1 … ..2 (1) = (2) Finding the relation Method Constructing the quadrilateral with the maximum area when given the lengths

11. consider triangle AEC from law of cosine then … .(3) thus From 1=3 Finding radius of circle Method Constructing the quadrilateral with the maximum area when given the lengths

12. finding , , and giving is the angle between radius of circle in triangle CED is the angle between radius of circle in triangle AED is the angle between radius of circle in triangle AEB is the angle between radius of circle in triangle BEC Consider triangle CED of law of cosine then thus In the same way Finding the angle at the center of circle Method Constructing the quadrilateral with the maximum area when given the lengths

13. consider then … .(1) (1)+(2) thus … .(2) Finding the relation of angles Method Constructing the quadrilateral with the maximum area when given the lengths

14. The relationship between angles and sides of the quadrilateral in the circle when the angle is between two sides that are adjacent sides. The first result Constructing the quadrilateral with the maximum area when given the lengths