Sun, 20 Jun
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# 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,
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
$\frac{1}{2}$ . d . (h1 + h2)
Perimeter = s1 + s2 + s3 + s4
d=diagonal,
h=altitude,
s=side
Circle Area = πr2
Perimeter = 2πr
π=3.141592,
Ellipse Area = πr1r2 π=3.141592,
Cube Volume = a3
Surface Area = 6a2
Diagonal =
$\sqrt{3}$ a
a=side
Cuboid Volume = l . b . h
Surface Area = 2 (lb + bh + lh)
Diagonal =
l=length,
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,
h=height
Cylinder Volume = πr2h
Curved surface area = 2πrh
Total surface area = 2πr(r + h)
π=3.141592,
h=altitude
Sphere Volume =
$\frac{4}{3}$ πr3
Surface Area = 4πr2
π=3.141592,
Hemi-sphere Area =
$\frac{2}{3}$ πr3
Curved surface Area = 2πr2
Total surface area = 3πr2
π=3.141592,