Mensuration

Mensuration is the branch of Mathematics which deals with geometric shapes and their properties like area, perimeter and volume etc.

Name	Shape	Formulae	Illustrations
Triangle		Area = $\frac{1}{2}$ . b . h Area = $\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$ Perimeter = (a + b + c)	b=base, h = altitude, s=semi-perimeter, a=b=c=sides
Square		Area = s2 Perimeter = 4s	s=side
Rectangle		Area = l . b Perimeter = 2 . (l + b)	l=length, b=breadth
Rhombus		Area = $\frac{1}{2}$ . d1 . d2 Perimeter = 4s	d=diagonals
Parallelogram		Area = b . h Perimeter = 2 . (a + b)	b=base, h=altitude, a=side
Trapezium		Area = $\frac{1}{2}$ . (a + b) . h Perimeter = a + b + c + d	a=b=parallel sides, c=d=non-parallel sides, h = altitude
Quadrilateral		Area = $\frac{1}{2}$ . d . (h1 + h2) Perimeter = s1 + s2 + s3 + s4	d=diagonal, h=altitude, s=side
Circle		Area = πr2 Perimeter = 2πr	π=3.141592, r=radius
Ellipse		Area = πr1r2	π=3.141592, r=radius
Cube		Volume = a3 Surface Area = 6a2 Diagonal = $\sqrt{3}$ a	a=side
Cuboid		Volume = l . b . h Surface Area = 2 (lb + bh + lh) Diagonal = $\sqrt{l^2 + b^2 + h^2}$	l=length, b=breadth, h=height
Cone		Slant Height (l) = $\sqrt{r^2+h^2}$ Volume = $\frac{1}{3}$ πr2h Curved surface area = πrl Total surface area = πr2 + πrl	l=slant height, π=3.141592, r=radius, h=height
Cylinder		Volume = πr2h Curved surface area = 2πrh Total surface area = 2πr(r + h)	π=3.141592, r=radius, h=altitude
Sphere		Volume = $\frac{4}{3}$ πr3 Surface Area = 4πr2	π=3.141592, r=radius
Hemi-sphere		Area = $\frac{2}{3}$ πr3 Curved surface Area = 2πr2 Total surface area = 3πr2	π=3.141592, r=radius