Mensuration is one of the branches of mathematics.This means measurement.It is is being done in our life in many situations.

For example,

A Length of cloth we need for stitching,the area of a wall which is being painted, perimeter of the circular garden to be fenced, quantity of water needed to fill the tank. For these kind of activities, we are doing measurements for further needs.

Here, we are going to cover three areas here.

1.Perimeter

2.Area

3.Volume

Apart from the examples and practice questions in the above three areas, we also give calculators in this topic which can be used by the students to check their answers which they have found for the questions they have.You can use any of the given calculators to get answer for your questions in seconds.

For example, in his development of integration and calculus, he tried to find a value for π by using circumscribed and inscribed polygons, eventually using 96 sided polygons inside and outside a circle to generate a value for Pi of between 31⁄7 (approximately 3.1429) and 310⁄71 (approximately 3.1408). This range of values is extremely accurate, as the actual value is 3.1416. This is just one example of his inventions.

In this topic we are going study about perimeter, area and volume of different shapes like a cylinder, cone, sphere, hemisphere etc..These shapes are called geometric shapes.

**Circle : **

**Formulas : **

Area of circle = Πr^{2}

Circumference of circle = 2Πr

Example problems of area of circle

Example problems of circumference of circle

**Semicircle : **

**Formulas : **

Area of semicircle = Πr^{2 }/ 2

Circumference of circle = Πr

Example problems on semi circle

**Quadrant : **

**Formulas : **

Area of quadrant = Πr^{2 }/ 4

Example problems on quadrant

**Equilateral Triangle :**

**Formulas : **

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

Perimeter of equilateral triangle = 3a

Example problems on equilateral triangle

**Scalene Triangle :**

**Formulas : **

Area of scalene triangle = √[s(s-a)(s-b)(s-c)]

Perimeter of scalene triangle = a + b + c

Example problems on scalene triangle

**Right Triangle :**

**Formula : **

Area of right triangle = (b x h) / 2

**Parallelogram :**

**Formulas : **

Area of parallelogram = b x h

Perimeter of parallelogram = 2(a + b)

Example problems of perimeter of parallelogram

**Quadrilateral : **

**Formulas : **

Area of quadrilateral = (1/2) x d x (h_{1 }+ h_{2})

Perimeter of quadrilateral = a + b + c + d

Example problems of area of quadrilateral

**Rectangle : **

**Formulas : **

Area of rectangle = l x w

Perimeter of rectangle = 2(l + w)

Examples problems on area of rectangle

Examples of perimeter of rectangle

**Square :**

**Formulas : **

Area of square = a x a

Perimeter of square = 4a

Examples problems on area of square

Examples problems on perimeter of square

**Rhombus :**

**Formulas : **

Area of rhombus = (d_{1} x d_{2}) / 2

Perimeter of rhombus = 4a

Examples problems on area of rhombus

Examples problems on perimeter of rhombus

**Trapezoid : **

**Formulas : **

Area of trapezoid = h(a + b) / 2

Perimeter of trapezoid = a + b + c + d

Examples problems on area of trapezoid

**Sector : **

**Formulas : **

Length of arc (l) = (θ/360) ⋅ 2Πr

When we know the radius "r" of the circle and central angle "θ" of the sector :

Area of the sector = (θ/360°) ⋅ Π r^{2}

When we know the radius "r" of the circle and arc length "l":

Area of the sector = (l ⋅ r) / 2

**Cylinder :**

**Formulas : **

Curved surface area of cylinder = 2Πrh

Total surface area of cylinder = 2Πr(h + r)

Volume of cylinder = Πr^{2}h

**Cone :**

**Formulas : **

Curved surface area of cone = Πrl

Total surface area of cone = 2Πr(l + r)

Volume of cone = Πr^{2}h / 3

**Sphere :**

**Formulas : **

Surface area of sphere = 4Πr^{2}

Volume of sphere = 4Πr^{3} / 3

**Hemisphere :**

**Formulas : **

Curved surface area of hemisphere = 2Πr^{2}

Total surface area of hemisphere = 3Πr^{2}

Volume of hemisphere = 2Πr^{3} / 3

**18. Heron's Triangle Area Calculator**

**20. Regular Polygon Area Calculator**

**22. Circle Sector Area Calculator**

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