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# Mensuration Problems, Trick, Formula For All Competitive Exams

**Mensuration** is a branch of mathematics that deals with the measurement of areas and volumes of various geometrical figures Figures, for example, 3D shapes, cuboids, barrels, cones, and circles have volume and territory. **Mensuration** manages the improvement of recipes to quantify their regions and volumes.

# All About Mensuration

The area of a cube is obtained using the formula A = 4 x length squared. The volume of a cube is obtained using the formula V = length cubed.

The area of a cuboid is obtained using the formula A = 2 [lb + lh + bh] where l is the length, b is the breadth and h is the height of the cuboid. The volume of the cuboid is arrived at using the formula V = length x breadth x-height.

The bent surface zone of a correct roundabout chamber can be gotten utilizing A = 2πrh where h is the stature of the barrel and r is the span of the base of the chamber. The all-out surface region of the chamber is acquired utilizing A = 2πr [h+r], and the volume is landed at utilizing V = πr2h.

A cone has a bent surface region called the parallel surface territory. The volume of a cone is 33% the volume of a barrel with a similar stature and sweep of the base.

Region is communicated in square units, while volume is communicated in cubic units.

## Role of Mensuration in Mathematics

**Mensuration** is the part of mathematics which manages the investigation of various geometrical shapes, their zones, and Volume. In the broadest sense, it is about the procedure of estimation. It depends on the utilization of arithmetical conditions and geometric figurings to give estimation information with respect to the width, profundity, and volume of a given article or gathering of items. While the estimation results acquired by the utilization of mensuration are appraising as opposed to genuine physical estimations, the figurings are generally viewed as exceptionally precise.

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### Some Important Formulas of Mensuration

**Rectangle :**

- Area = lb

Perimeter = 2(l+b)

**Square :**

- Area = a×a

Perimeter = 4a

Parallelogram - Area = l × h

Perimeter = 2(l+b)

**Triangle :**

- Area =b×h/2 or √s(s-a)(s-b)(s-c)…………….where s=a+b+c/2

Right angle Triangle : - Area =1/2(bh)

Perimeter = b+h+d

**Isosceles right angle triangle :**

- Area = ½. a2

Perimeter = 2a+d……………………….where d=a√2

Equilateral Triangle : - Area = √3. a2/4 or ½(ah)….where h = √3/2

Perimeter = 3a

**Trapezium :**

- Area = 1/2h(a+b)

Perimeter = Sum of all sides

**Rhombus :**

- Area = d1 × d2/2

Perimeter = 4l

Quadrilateral - Area =1/2 × Diagonal × (Sum of offsets)

**Kite :**

- Area = d1×d2/2

Perimeter = 2 × Sum on non-adjacent sides

**Circle :**

- Area = πr^2 or πd^2/4

Circumference = 2πr or πd

Area of sector of a circle = (θπr^2 )/360

**Frustum :**

- Curved surface area = πh(r1+r2)

Surface area = π( r12+ h(r1+r2) + r22)

**Cube :**

- Volume: V = l3

Lateral surface area = 4a2

Surface Area: S = 6s2

Diagonal (d) = √3l

**Cuboid :**

- Volume of cuboid: lbh

Total surface area = 2 (lb + bh + hl) or 6l2

Length of diagonal =√(l^2+b^2+h^2)

**Right Circular Cylinder :**

- Volume of Cylinder = π r2 h

Lateral Surface Area (LSA or CSA) = 2π r h

Total Surface Area = TSA = 2 π r (r + h)

Volume of hollow cylinder = π r h(R2 – r2)

**Right Circular cone :**

- Volume = 1/3 π r2h

Curved surface area: CSA= π r l

Total surface area = TSA = πr(r + l )

**Sphere**

- Volume: V = 4/3 πr3

Surface Area: S = 4πr2

**Hemisphere :**

- Volume = 2/3 π r3

Curved surface area(CSA) = 2 π r2

Total surface area = TSA = 3 π r2

**Prism :**

- Volume = Base area x h

Lateral Surface area = perimeter of the base x h

**Pyramid:**

- The volume of a right pyramid = (1/3) × area of the base × height.

Area of the lateral faces of a right pyramid = (1/2) × perimeter of the base x slant height.

Area of the whole surface of a right pyramid = area of the lateral faces + area of the base.

**Tetrahedron :**

- Area of its slant sides = 3a2√3/4

Area of its whole surface = √3a2

Volume of the tetrahedron = (√2/12) a 3

**Regular Hexagon :**

- Area = 3√3 a2 / 2

Perimeter = 6a

**Some other Formula of Mensuration**

- Area of Pathway running across the middle of a rectangle = w(l+b-w)

A perimeter of Pathway around a rectangle field = 2(l+b+4w)

Area of Pathway around a rectangle field =2w(l+b+2w)

A perimeter of Pathway inside a rectangle field =2(l+b-4w)

Area of Pathway inside a rectangle field =2w(l+b-2w)

Area of four walls = 2h(l+b)

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