Mensuration formulas  All formulae
In mensuration, we often have to deal with the problem of finding the areas and perimeters of plane figures. So for that, we need to learn mensuration formulas. But before that let's have a look at some basic definitions of basic figures.
1. Rectangle: A quadrilateral with opposite sides equal and all the four angles equal to 90°.
2. Square: A quadrilateral with all sides equal and all the four angles equal to 90°.
3. Parrellelogram: A quadrilateral with opposite sides parallel and equal
4. Rhombus: A parallelogram with all four sides equal.
5. Trapezium: A quadrilateral with any one pair of opposite sides parallel.
6. Rightangled triangle: A triangle with one angle equal to 90°.
7. Isosceles triangle: A triangle with any two sides equal. In an isosceles triangle, opposite angles are equal.
8. Equilateral triangle: A triangle with all sides equal. In an equilateral triangle, all angles are equal, each being equal to 60.
Mensuration Formulas:
Square

· Area = Side x Side
· Side (S) = √Area
· Perimeter = 4(Side)
· Diagonal = (Side) x √2

Rectangle

· Area = l x b
· Perimeter = 2 (l + b)
· Diagonal = √l^{2 }+ b^{2}

Triangle

· Area = ½ x base x height
· Area = √s(sa)(sb)(sc)
Where, s = semiperimeter
= (a + b + c)/2

Area and perimeter of Right angled Isosceles Triangle

· Area = 1/2a^{2}
· Perimeter = (2a + √2a)
· Height = a/√2

Area of an Equilateral Triangle

· Area = (√3/4) x Side^{2} = (√3/4)a^{2}
· Altitude = (√3/2) x Side = (√3/2)a
· Perimeter = 3 x Side = 3a

Circle

· Circumference = 2pr = pD
· Area = (p/4) D^{2}

Semi Circle

· Area of semicircle = 1/2pr^{2}
· Perimeter = pr + 2r = pr + D

Volume of a cube

· Edge of cube = length=breadth=height=a
· Volume of a cube = (edge)^{3}=a^{3}
· Total surface Area = 6 x (edge)^{2}= 6a^{2}
· Diagonal of a cube = √3 x edge = √3a

Volume of a cuboid

· V = l x b x h
· Surface area = 2(lb + bh + hl)
· Diagonal = √l^{2} + b^{2} + h^{2}

Right Circular Cylinder

· Volume = pr^{2}h
· Curved Surface Area = 2prh
· Total Surface Area = 2prh + 2pr^{2} = 2pr(r + h)

Right Circular Cone

· Volume = 1/3pr^{2}h
· Curved Surface Area = prl
· Total surface Area = prl + pr^{2} = pr(l + r)

Sphere

· Volume = 4/3pr^{3}
· Surface Area = 4pr^{2}

Hemisphere

· Volume = 2/3pr^{3}
· Curved Surface Area = 2pr^{2}
· Total surface Area = 2pr^{2} + pr^{2} = 3pr^{2}

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