രൂപം
ചിത്രം
x ¯ {\displaystyle {\bar {x}}}
y ¯ {\displaystyle {\bar {y}}}
Area
ചതുര ക്ഷേത്രം
align="center" |
b 2 {\displaystyle {\frac {b}{2}}}
h 2 {\displaystyle {\frac {h}{2}}}
b h {\displaystyle {bh}}
പൊതുവായ ത്രികോണ ക്ഷേത്രം
b 3 {\displaystyle {\frac {b}{3}}}
h 3 {\displaystyle {\frac {h}{3}}}
b h 2 {\displaystyle {\frac {bh}{2}}}
സമഭുജ-ത്രികോണ ക്ഷേത്രം
l 2 {\displaystyle {\frac {l}{2}}}
h 3 {\displaystyle {\frac {h}{3}}}
l h 2 {\displaystyle {\frac {lh}{2}}}
മട്ടത്രികോണ ക്ഷേത്രം
b 3 {\displaystyle {\frac {b}{3}}}
h 3 {\displaystyle {\frac {h}{3}}}
b h 2 {\displaystyle {\frac {bh}{2}}}
വൃത്ത ക്ഷേത്രം
0 {\displaystyle 0}
0 {\displaystyle 0}
π r 2 {\displaystyle {\pi r^{2}}}
വൃത്ത ചതുർത്ഥാംശ ക്ഷേത്രം [1]
4 r 3 π {\displaystyle {\frac {4r}{3\pi }}}
4 r 3 π {\displaystyle {\frac {4r}{3\pi }}}
π r 2 4 {\displaystyle {\frac {\pi r^{2}}{4}}}
അർദ്ധവൃത്ത ക്ഷേത്രം [2]
0 {\displaystyle 0}
4 r 3 π {\displaystyle {\frac {4r}{3\pi }}}
π r 2 2 {\displaystyle {\frac {\pi r^{2}}{2}}}
വൃത്താംശം
2 r sin ( α ) 3 α {\displaystyle {\frac {2r\sin(\alpha )}{3\alpha }}}
0 {\displaystyle \,\!0}
α r 2 {\displaystyle \,\!\alpha r^{2}}
വൃത്തഖണ്ഡം
4 r sin 3 ( α ) 3 ( 2 α − sin ( 2 α ) ) {\displaystyle {\frac {4r\sin ^{3}(\alpha )}{3(2\alpha -\sin(2\alpha ))}}}
0 {\displaystyle \,\!0}
r 2 2 ( 2 α − sin ( 2 α ) ) {\displaystyle {\frac {r^{2}}{2}}(2\alpha -\sin(2\alpha ))}
വലയാംശം
2 sin ( α ) 3 α r 2 3 − r 1 3 r 2 2 − r 1 2 {\displaystyle {\frac {2\sin(\alpha )}{3\alpha }}{\frac {r_{2}^{3}-r_{1}^{3}}{r_{2}^{2}-r_{1}^{2}}}}
0 {\displaystyle \,\!0}
α ( r 2 2 − r 1 2 ) {\displaystyle \alpha (r_{2}^{2}-r_{1}^{2})}
പാദവൃത്ത ചാപം
The points on the circle x 2 + y 2 = r 2 {\displaystyle \,\!x^{2}+y^{2}=r^{2}} and in the first quadrant
2 r π {\displaystyle {\frac {2r}{\pi }}}
2 r π {\displaystyle {\frac {2r}{\pi }}}
L = π r 2 {\displaystyle L={\frac {\pi r}{2}}}
അർദ്ധവൃത്ത ചാപം
The points on the circle x 2 + y 2 = r 2 {\displaystyle \,\!x^{2}+y^{2}=r^{2}} and above the x {\displaystyle \,\!x} axis
0 {\displaystyle \,\!0}
2 r π {\displaystyle {\frac {2r}{\pi }}}
L = π r {\displaystyle L=\,\!\pi r}
വൃത്തചാപം
The points on the curve (in polar coordinates) ρ = r {\displaystyle \,\!\rho =r} , from θ = − α {\displaystyle \,\!\theta =-\alpha } to θ = α {\displaystyle \,\!\theta =\alpha }
ρ sin ( α ) α {\displaystyle {\frac {\rho \sin(\alpha )}{\alpha }}}
0 {\displaystyle \,\!0}
L = 2 α ρ {\displaystyle L=\,\!2\alpha \rho }
ദീർഘവൃത്തക്ഷേത്രം
0 {\displaystyle 0}
0 {\displaystyle 0}
π a b {\displaystyle {\pi ab}}
ദീർഘവൃത്തചതുർത്ഥാംശ ക്ഷേത്രം
4 a 3 π {\displaystyle {\frac {4a}{3\pi }}}
4 b 3 π {\displaystyle {\frac {4b}{3\pi }}}
π a b 4 {\displaystyle {\frac {\pi ab}{4}}}
അർദ്ധദീർഘവൃത്ത ക്ഷേത്രം
0 {\displaystyle \,\!0}
4 b 3 π {\displaystyle {\frac {4b}{3\pi }}}
π a b 2 {\displaystyle {\frac {\pi ab}{2}}}
പരവലയ ക്ഷേത്രം
The area between the curve y = h b 2 x 2 {\displaystyle \,\!y={\frac {h}{b^{2}}}x^{2}} and the line y = h {\displaystyle \,\!y=h}
0 {\displaystyle \,\!0}
3 h 5 {\displaystyle {\frac {3h}{5}}}
4 b h 3 {\displaystyle {\frac {4bh}{3}}}
അർദ്ധപരവലയക്ഷേത്രം
The area between the curve y = h b 2 x 2 {\displaystyle y={\frac {h}{b^{2}}}x^{2}} and the y {\displaystyle \,\!y} axis, from y = 0 {\displaystyle \,\!y=0} to y = h {\displaystyle \,\!y=h}
3 b 8 {\displaystyle {\frac {3b}{8}}}
3 h 5 {\displaystyle {\frac {3h}{5}}}
2 b h 3 {\displaystyle {\frac {2bh}{3}}}
Parabolic spandrel
The area between the curve y = h b 2 x 2 {\displaystyle \,\!y={\frac {h}{b^{2}}}x^{2}} and the x {\displaystyle \,\!x} axis, from x = 0 {\displaystyle \,\!x=0} to x = b {\displaystyle \,\!x=b}
3 b 4 {\displaystyle {\frac {3b}{4}}}
3 h 10 {\displaystyle {\frac {3h}{10}}}
b h 3 {\displaystyle {\frac {bh}{3}}}
General spandrel
The area between the curve y = h b n x n {\displaystyle y={\frac {h}{b^{n}}}x^{n}} and the x {\displaystyle \,\!x} axis, from x = 0 {\displaystyle \,\!x=0} to x = b {\displaystyle \,\!x=b}
n + 1 n + 2 b {\displaystyle {\frac {n+1}{n+2}}b}
n + 1 4 n + 2 h {\displaystyle {\frac {n+1}{4n+2}}h}
b h n + 1 {\displaystyle {\frac {bh}{n+1}}}