രൂപം
ചിത്രം
x
¯
{\displaystyle {\bar {x}}}
y
¯
{\displaystyle {\bar {y}}}
Area
ചതുര ക്ഷേത്രം
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}}}
അർത്ഥവൃത്ത 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}}
2
r
π
{\displaystyle {\frac {2r}{\pi }}}
2
r
π
{\displaystyle {\frac {2r}{\pi }}}
L
=
π
r
2
{\displaystyle L={\frac {\pi r}{2}}}
അർത്ഥവൃത്ത ചാപം
The points on the circle
x
2
+
y
2
=
r
2
{\displaystyle \,\!x^{2}+y^{2}=r^{2}}
x
{\displaystyle \,\!x}
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}
θ
=
−
α
{\displaystyle \,\!\theta =-\alpha }
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}}}
അർത്ഥദീർഘവൃത്ത ക്ഷേത്രം
0
{\displaystyle \,\!0}
4
b
3
π
{\displaystyle {\frac {4b}{3\pi }}}
π
a
b
2
{\displaystyle {\frac {\pi ab}{2}}}
പരവലയ ക്ഷേത്രംThe area between the curve
y
=
h
b
2
x
2
{\displaystyle \,\!y={\frac {h}{b^{2}}}x^{2}}
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}}
y
{\displaystyle \,\!y}
y
=
0
{\displaystyle \,\!y=0}
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}}
x
{\displaystyle \,\!x}
x
=
0
{\displaystyle \,\!x=0}
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}}
x
{\displaystyle \,\!x}
x
=
0
{\displaystyle \,\!x=0}
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}}}
