Perimeter

Perimeter Given (a+b+c)=k 

Find 

Maximum area of triangle
(a=b=c) 

Put value of side a 

Put value of side b 

Value of side c 

Value of angle ∠c between a & b in radian 

Value of angle ∠c between a & b in degree 

Area of Triangle▲ 

% area of ▲ / maximum area of ▲ 

3rd side of triangle can be found from
solution of the following equation :Ax^{4} + Bx^{2 } + C=0
or
x^{4}
+x^{2 }
+=0 

Solution : x4 

Solution : x4a 

Solution : x3 

Solution : x3a 

Maximum area of
quadrilateral (a=b=c=d) 

side a 

side b 

angle between a & b in degree 

diagonal e 

side c 

side d 

area of triangle abe 

area of triangle cde 

area of quadrilateral 

% area of ▮ / maximum area of ▮ 

Maximum area of Rectangle(side1=side2) 

Put value of one side 

Value of other side 

Area of Rectangle 

% area of ▮ / maximum area of ▮ 

area of Circle 

Radius of Circle 

semimajor + semiminor axis≅k/PI
of Ellipse 

Semi major Axis (a4) 

Semiminor Axis (b4) 

Find discount factor upto 3rd term 

h/4 + h^{2} / 64 + h^{3} /256 +.....+.....infinite series) 

where h=(ab/a+b)^{2} 

Revised Semi major Axis 

Revised Semi minor Axis 

Revised Perimeter 

Area of Ellipse 

% area of ellipse / maximum area of ellipse 



*To find side c of a triangle when a,b are given and in between angle say θ
is given . area=(ab/2)sinθ .Now area formula from the sides is
(X1+c)(X2+c)(X2+c)(X1c) =16 A*A where X1=a+b,X2=ba; simplifying, c^{4}
(X1^{2} +X2^{2})c^{2} +[(X1^{2} *X2^{2} )+16A*A]=0
or c*c=y and y^{2}
(X1^{2} +X2^{2})y +[(X1^{2} *X2^{2} )+16A*A]=0
or Ay^{2} +By+C=0 where A=1, B = (X1^{2} +X2^{2})
=2(a*a+b*b) and C=[(X1^{2} *X2^{2} )+16A*A] = (a+b)^{2}*(ba)^{2}
+16A*A;
* in ellipse, R=(periR)*dfactor or R=peri*dfactor/(1+dfactor) 



