Learning Ashram

Geometric Formulas

GEOMETRIC FORMULAS
RECTANGLE OF LENGTH b AND WIDTH a

Area = ab
Perimeter = 2a + 2b
PARALLELOGRAM OF ALTITUDE h AND BASE b

Area = bh = ab sin θ
Perimeter = 2a + 2b
TRIANGLE OF ALTITUDE h AND BASE b

Area = ½bh = ½ab sin θ
      = √s(s-a)(s-b)(s-c)
where s = ½(a + 6 + c) = semiperimeter
Perimeter = a + b + c
TRAPEZOID OF ALTITUDE h AND PARALLEL a AND b
Area = ½h(a + b)
Perimeter= a+b+h(1/sinθ + 1/sinθ)
       =a+b+h(cscθ+cscθ)
REGULAR POLYGON OF n SIDE EACH OF LENGTH b

Area=¼nb² cot π/n =¼nb² cos(π/n)/sin(π/n)
Perimeter =nb
CIRCLE OF RADIUS r

Area = πr²
Perimeter=2πr²
SECTOR OF CIRCLE OF RADIUS r

Area=½r²θ   [θ in radians ]
Arc length s=rθ
RADIUS OF CIRCLE INSCRIBED IN A TRIANGLE OF SIDE a,b,c

r=√s(s-a)(s-b)(s-c)/s
Where s= ½(a+b+c)=semiperimeter
RADIUS OF CIRCLE CIRCUMSCRIBING A TRIANGLE OF SIDE a,b,c

R=abc / 4√s(s-a)(s-b)(s-c)
where s= ½(a+b+c)=semiperimeter
REGULAR POLYGON OF n SIDES INSCRIBED IN CIRCLE OF RADIUS r


REGULAR POLYGON OF n SIDES CIRCUMSCRIBING A CIRCLE OF RADIUSr

SEGMENT OF CIRCLE OF RADIUSr

Area of shaded part = ½ (e — sin θ)
ELLIPSE OF SEMI-MAJOR AXIS a AND SEMI-MINOR AXIS b

SEGMENT OF A PARABOLA

RECTANGULAR PARALLELEPIPED OF LENGTH a, HEIGHT I, WIDTH c

Volume = abc
Surface area = 2{ab + ac + be)
PARALLELEPIPED OF CROSS-SECTIONAL AREA A AND HEIGHT h

Volume = Ah = abc sin θ
SPHERE OF RADIUS r

RIGHT CIRCULAR CYLINDER OF RADIUS r AND HEIGHT h

Volume = πh
Lateral surface area = 2πrh
CIRCULAR CYLINDER OF RADIUS r AND SLANT HEIGHT l

CYLINDER OF CROSS-SECTIONAL AREA A AND SLANT HEIGHT l
Volume   = Ah = Al sin θ
RIGHT CIRCULAR CONE OF RADIUS r AND HEIGHT h

PYRAMID OF BASE AREA A AND HEIGHT h

Volume   = Ah
SPHERICAL CAP OF RADIUS r AND HEIGHT h
Volume (shaded in figure) =π(3r — h)
Surface area = 2πrh
FRUSTRUM OF RIGHT CIRCULAR CONE OF RADII a,b AND HEIGHT h

SPHERICAL TRIANGLE OF ANGLES A,B,C ON SPHERE OF RADIUS r

Area of triangle ABC = (A + B + C - πr)r²
TORUS OF INNER RADIUS a AND OUTER RADIUS b

Volume =¼π²(a + b)(b - a)²
Surface area= π²(b² - a² )
ELLIPSOID OF SEMI-AXES a,b,e

Volume =¾ π abc
PARABOLOID OF REVOLUTION

Volume =½πb²a