Mensuration

May 30 • Bank, Banking Awareness Notes • 226 Views • No Comments on Mensuration

Area: area of a bounded figure is the space covered by it.
Perimeter: The length of the boundary of a closed figure is called perimeter
Triangle: A plane figure bounded by three straight lines is called a triangle

Area of a triangle = 12base height = 12CDAB
s(s-a) (s-b) (s-c)
And s = a + b + c2
Where a, b, c are the lengths of the sides of triangle

Equilateral triangle if all the three sides of a triangle are equal , then there is an equilateral triangle

Area of an equilateral triangle = 34a2
Perimeter of an equilateral triangle with side a = 3a

Isosceles triangle if at least two sides of a triangle are equal, there is a isosceles triangle
Area of isosceles triangle = a44b2 – a2
And height of isosceles triangle, h = b2 – a24
Perimeter of isosceles triangle = 2b + a

Square:

Area of a square = (side)2= a2 or
d22 where d is the diagonal of a square
Perimeter of a square = 4a
Diagonal of a square = 2a
Area of a path which is outside of a square of uniform width x = 4×2+ 4ax
Area of a path which is inside of a square of uniform width x = 4ax – 4×2
Perimeter of a path which is outside of a square of uniform width x = 4(a + 2x)
Perimeter of a path which is inside of a square of uniform width x = 4(a- 2x)

Rectangle:

Area of a rectangle = lb, where l is the length of a rectangle and b is the breadth of a rectangle
Perimeter of a rectangle = 2(l + b)
Diagonal of a rectangle, d = l2 + b2
Area of a path which is outside of a rectangle of uniform width x =4×2+2lx + 2bx
Area of a path which is inside of a rectangle of uniform width x = 2lx + 2bx – 4×2
Perimeter of a path which is outside of a square of uniform width x = 2(l + b + 2x)
Perimeter of a path which is outside of a square of uniform width x = 2(l + b – 2x)

Parallelogram:

Area of parallelogram = 12baseheight = 12bh

Rhombus: it is a parallelogram whose all sides are equal
Its diagonal bisect each other at right angle.

Area of rhombus = 12 product of diagonals = 12d1d2 or
Area = 12bh
Where b is the side of rhombus, h is the height and d1,d2are the diagonals of the rhombus
Perimeter of rhombus = 4b
Side of rhombus = ( d12)2 + ( d22)2

Trapezium:

Area of trapezium = 12height (sum of parallel sides)
Median of trapezium = 12(sum of parallel sides)
Median is the line segment joining the midpoints of non parallel side

Circle:

Area of a circle= r2
Diameter (d) = 2r
Circumference = 2r
Area of a sector =360 r2
Length of arc = 360 2r
Area of the ring or circular path = (R+r) (R-r)

Cube:

Volume of a cube = a3
Diagonal of a cube = 3a
Surface area of a cube = 6a2
Area of four walls = 4a2

Cuboid:

Volume of a cuboid = lbh
Diagonal of a cuboid = l2+ b2+h2
Surface area of a cuboid = 2(lb + bh + hl)
Area of four walls = 2(lh + bh)

Cylinder:

Volume of a cylinder = r2h
Curved surface area = 2rh
Total surface area = 2r(r + h)

Cone:

Volume of a cone = 13r2h
Curved surface area = rl
Total surface area = r (l + r)
Slant height = h2+ r2

Sphere:

Volume of a sphere = 43r3
Surface area = 4r2

Hemisphere:

Volume of a hemisphere = 23r3
Curved surface area = 2r2
Total surface area = 3r2

Frustum of a cone

Volume = 13h(r2+R2+ r.R)
Surface area = (r + R)(R -r)2+h2
Total surface area = (r + R)(R -r)2+h2 + r2 + R2
Slant height, l = (R -r)2+h2

Right pyramid

Volume of a pyramid = 13(area of the base)height
Lateral surface area of a pyramid = 12(perimeter of base) slant height
Total surface area of a pyramid = lateral surface area + area of the base

Regular tetrahedron it is a polyhedron with four equilateral triangle faces
Let the edge of a regular tetrahedron is a
Volume = 212a3
Lateral surface area = 334a2
Total surface area = 3a2

Relation between edges, vertices and faces of a polyhedron
Faces + edges = vertices – 2

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