MENSURATION
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
Area of circle = πr2
Circumference of circle = 2πr
Example problems of area of circle
Example problems of circumference of circle
Semi Circle
Area of semicircle = πr2/2
Circumference of circle = πr
Example problems on semi circle
Quadrant
Area of quadrant = πr2/4
Equilateral Triangle
Area of equilateral triangle = (√3/4)a2
Perimeter of equilateral triangle = 3a
Example problems on equilateral triangle
Scalene Triangle
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
Area of right triangle = (b x h)/2
Parallelogram
Area of parallelogram = b x h
Perimeter of parallelogram = 2(a + b)
Example problems of perimeter of parallelogram
Quadrilateral
Area of quadrilateral = (1/2) x d x (h1 + h2)
Perimeter of quadrilateral = a + b + c + d
Rectangle
Area of rectangle = l x w
Perimeter of rectangle = 2(l + w)
Examples of perimeter of rectangle
Square
Area of square = a x a
Perimeter of square = 4a
Examples problems on area of square
Examples problems on perimeter of square
Rhombus
Area of rhombus = (d1 x d2)/2
Perimeter of rhombus = 4a
Examples problems on area of rhombus
Examples problems on perimeter of rhombus
Trapezoid
Area of trapezoid = h(a + b)/2
Perimeter of trapezoid = a + b + c + d
Examples problems on area of trapezoid
Sector
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°) ⋅ πr2
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
Curved surface area of cylinder = 2πrh
Total surface area of cylinder = 2πr(h + r)
Volume of cylinder = πr2h
Cone
Curved surface area of cone = πrl
Total surface area of cone = 2πr(l + r)
Volume of cone = πr2h/3
Sphere
Surface area of sphere = 4πr2
Volume of sphere = 4πr3/3
Hemisphere
Curved surface area of hemisphere = 2πr2
Total surface area of hemisphere = 3πr2
Volume of hemisphere = 2πr3/3
Mensuration Calculators
18. Heron's Triangle Area Calculator
20. Regular Polygon Area Calculator
22. Circle Sector Area Calculator
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