Question Number 209314 by SonGoku last updated on 06/Jul/24
![](https://www.tinkutara.com/question/34370.png)
Commented by SonGoku last updated on 06/Jul/24
![How to find the of this polygon?](https://www.tinkutara.com/question/Q209315.png)
Commented by mr W last updated on 07/Jul/24
![you can only find the perimeter of the polygon, nothing else of it.](https://www.tinkutara.com/question/Q209326.png)
Commented by SonGoku last updated on 07/Jul/24
![So the only way to determine the diagonal of ang irreular polygon, like the one in the image, is onlyo thrugh practice? In other words, in the field?](https://www.tinkutara.com/question/Q209333.png)
Commented by Frix last updated on 07/Jul/24
![Diagonal=d 18<d<35 ((√(197319))/4)<area≤((√(1278519))/4) (min at d=35, max at d=((√(638290))/(29)))](https://www.tinkutara.com/question/Q209334.png)
Commented by Frix last updated on 07/Jul/24
![For 1 triangle you need at least 3 measurements. In this case, you need 1 additional measurment for one of the triangles, the rest follows.](https://www.tinkutara.com/question/Q209344.png)
Commented by SonGoku last updated on 08/Jul/24
![But, how did you at these calculations?](https://www.tinkutara.com/question/Q209354.png)
Commented by Frix last updated on 08/Jul/24
![1^(st) triangle 10, 28, d ⇒ 18<d<38 2^(nd) triangle 15, 20, d ⇒ 5<d<35 ⇒ 18<d<35 Area of triangle a, b, c =((√((a+b+c)(b+c−a)(a+c−b)(a+b−c)))/4) Area of 1^(st) triangle A_1 =((√(−d^4 +1768d^2 −467856))/4) Area of 2^(nd) triangle A_2 =((√(−d^4 +1250d^2 −30625))/4) For the minimum obviously d=18 ⇒ A_1 =0 For the maximum I used differentiation](https://www.tinkutara.com/question/Q209386.png)
Commented by mr W last updated on 08/Jul/24
![maximum area is when the quadilateral is cyclic. s=((a+b+c+d)/2)=((10+28+15+20)/2)=36.5 A_(max) =(√((s−a)(s−b)(s−c)(s−d))) =(√((36.5−10)(36.5−28)(36.5−15)(36.5−20))) =((√(1278519))/4) see also Q30233](https://www.tinkutara.com/question/Q209392.png)
Commented by SonGoku last updated on 09/Jul/24
![Very sophisticated. Congratulations I willa study. Thank you.](https://www.tinkutara.com/question/Q209409.png)
Commented by SonGoku last updated on 09/Jul/24
![So, can I use this formula to determine the area of any quadrilateral?](https://www.tinkutara.com/question/Q209410.png)
Commented by mr W last updated on 09/Jul/24
![no! it′s only for so−called cyclic quadrilaterals. generally a quadrilateral is not uniquely defined when only its four sides are given. you need an additional condition.](https://www.tinkutara.com/question/Q209412.png)