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

Worksheet for length of arc

**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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You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**