# Mensuration

**Mensuration** is the branch of Mathematics which deals with the study of geometric shapes, their **area**, **volume** and different parameters in geometric objects.

### Rectangle

**1.** Area of rectangle = length(l) * Breath(b) = l x b

**2.** Perimeter of a rectangle = 2 * (Length(l) + Breath(b)) = 2(l + b)

### Square

**3.** Area of a square = Length (l) * Length (l) = l x l

**4.** Perimeter of a square = 4 * Length (l) = 4 x l

### Parallelogram

**5.** Area of a parallelogram = Length(l) * Height(h) = l x h

**6.** Perimeter of a parallelogram = 2 * (length(l) + Breadth(b)) = 2(l + b)

### Triangle

**7.** Area of a triangle = (Base(b) * Height(b)) / 2 = ½ x b x h

Perimeter = (a + b + c)

Area of triangle = √{s(s-a)(s-b)(s-c)} [Hero’s formula]

**8.** Area of triangle = ½ab∠C = ½bc∠A = ½ac∠B

**9.** Area of isosceles triangle = (b/4) * √(4a^{2}-b^{2})

### Trapezium

**10.** Area of trapezium = ½(a + b)h

**11.** Perimeter of a trapezium = sum of all sides

### Rhombus

**12.** Area of rhombus = Product of diagonals / 2

**13.** Perimeter of a rhombus = 4 * length

### Quadrilateral

**14.** Area of quadrilateral = ½ * Diagonal * (Sum of offsets)

### Kite

**15.** Area of a Kite = ½ * product of its diagonals

**16.** Perimeter of a Kite = 2 * Sum on non-adjacent sides

### Circle

**17.** Area of a Circle = πr^{2} = πd^{2}/4

**18.** Circumference of a Circle = 2πr = πd

### Cube and Cuboid

**19.** Total surface area of cuboid = 2(lb + bh + lh)

**20.** Total surface area of cube = 6 * l^{2}

**21.** Length of diagonal of cuboid = √(l^{2}+b^{2}+h^{2})

**22.** Length of diagonal of cube = √(3l)

**23.** Volume of cuboid = l * b * h

**24.** Volume of cube = l * l * l

### Cone

**25.** Area of base of a cone = πr^{2}

**26.** Curved surface area of a cone = C = πrl

**27.** Total surface area of a cone = πr(r + l)

**28.** Volume of right circular cone = (1/3) * πr^{2}h

### Prism

**29.** Surface area of triangular prism = (P * height) + (2 * area of triangle)

**30.** Surface area of polygonal prism = (Perimeter of base * height) + (Polygonal base area * 2)

**31.** Lateral surface area of prism = Perimeter of base * height

**32.** Volume of Triangular prism = Area of the triangular base * height

### Cylinder

**33.** Curved surface area of a cylinder = 2πrh

**34.** Total surface area of a cylinder = 2πr(r + h)

**35.** Volume of a cylinder = πr^{2}h

### Sphere

**36.** Surface area of sphere = 4πr^{2} = πd^{2}

**37.** Volume of a sphere = (4/3) * πr^{3} = 1/6 * πd^{3}

### Other Figures

**38.** Volume of hollow cylinder = πrh(R^{2}-r^{2})

**39.** Surface area of a right square pyramid = a √(4b^{2} - a^{2})

**40.** Volume of a right square pyramid = (1/3) * b^{2}h

**41.** Area of a regular hexagon = 3√3a^{2})/2

**42.** Area of equilateral triangle = (√3/4) * a^{2}

**43.** Curved surface area of a Frustums = πh(r_{1} + r_{2})

**44.** Total surface area of a Frustums = π (r_{1}^{2} + h(r_{1}+r_{2}) + r_{2}^{2})

**45.** Curved surface area of a Hemisphere = 2πr^{2}

**46.** Total surface area of a Hemisphere = 3πr^{2}

**47.** Volume of a Hemisphere = (2/3) * πr^{3} = (1/12) * πd^{3}

**48.** Area of sector of a circle = (θr^{2}π)/360