Circle always possess the largest area for the given perimeter of any two dimensional shape.
Lets consider the shape of circle, square, ellipse, octagon having the same perimeter. Let us consider perimeter to be 10.
This can be found by substituting in algebraic terms.
Area of the circle is pi.r2 where r = p/(2xpi) , r = 10 / (2 x 3.14) =10/(6.28) = 1.59
substituting in the equation pi.r2 = 3.14 x (1.59)2= 3.14 x 2.52 = 7.9
Area of the square is s2, s= p2/16 , = 102 /16 = 100 / 16 = 6.2
Area of the octagon is (2 + 2√2)s2, S = p2/64
So the area of an octagon is (2 + 2√2)p2/64
When substituting the values of perimeter, (2 + 2√2) 102/64 = 7.5
Area of the octagon is = 7.5
Thus the result clearly proves that circle will always have the largest area with any two dimensional shape having the same perimeter.
The number of possibility chess moves after the white move's is 20 (ie 4 knight moves and 16 moves o...
Your twin sibling will get more youthful than you when he returns from the space travel. If your twi...
Grigori Yakovlevich Perelman is a Russian mathematician, who made a history in Riemannian geometry a...
Daily Maths Topic Today - largest area by shape.