Mathematics Mensuration 2D & 3D Formulas with Basics & Notes PDF, Candidates can download Maths Mensuration 2D Formulas Notes PDF Free, SSC CGL Mathematic 3D Formulas pdf Download
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Mathematics Mensuration 2D Formulas Complete Details
Rectangle
A four-sided shape that is made up of two pairs of parallel lines and that has four right angles; especially: a shape in which one pair of lines is longer than the other pair.
The diagonals of a rectangle bisect each other and are equal.
Area of rectangle = length x breadth = l x b
OR Area of rectangle =
if one sides (l) and diagonal (d) are given.
OR Area of rectangle =
if perimeter (P) and diagonal (d) are given.
Perimeter (P) of rectangle = 2 (length + breadth) = 2 (l + b).
OR Perimeter of rectangle =
if one sides (l) and diagonal (d) are given.
Square
A four-sided shape that is made up of four straight sides that are the same length and that has four right angles.
The diagonals of a square are equal and bisect each other at 900.
(a) Area (a) of a square
Perimeter (P) of a square
= 4a, i.e. 4 x side
Length (d) of the diagonal of a square
Circle
A circle is the path traveled by a point which moves in such a way that its distance from a fixed point remains constant.
The fixed point is known as center and the fixed distance is called the radius.
(a) Circumference or perimeter of circle =
where r is radius and d is diameter of circle
(b) Area of circle
is radius
is circumference
circumference x radius
(c) Radius of circle =
Sector :
A sector is a figure enclosed by two radii and an arc lying between them.
here AOB is a sector
length of arc AB= 2πrΘ/360°
Area of Sector ACBO=1/2[arc AB×radius]=πr×r×Θ/360°
Ring or Circular Path:
R=outer radius
r=inner radius
area=π(R2-r2)
Perimeter=2π(R+r)
Rhombus
Rhombus is a quadrilateral whose all sides are equal.
The diagonals of a rhombus bisect each other at 900
Area (a) of a rhombus
= a * h, i.e. base * height
Product of its diagonals
since d22
since d22
Perimeter (P) of a rhombus
= 4a, i.e. 4 x side
Where d1 and d2 are two-diagonals.
Side (a) of a rhombus
Parallelogram
A quadrilateral in which opposite sides are equal and parallel is called a parallelogram. The diagonals of a parallelogram bisect each other.
Area (a) of a parallelogram = base × altitude corresponding to the base = b × h
Area (a) of parallelogram
where a and b are adjacent sides, d is the length of the diagonal connecting the ends of the two sides and
In a parallelogram, the sum of the squares of the diagonals = 2
(the sum of the squares of the two adjacent sides).
i.e.,
Perimeter (P) of a parallelogram
= 2 (a+b),
Where a and b are adjacent sides of the parallelogram.
Trapezium (Trapezoid)
A trapezoid is a 2-dimensional geometric figure with four sides, at least one set of which are parallel. The parallel sides are called the bases, while the other sides are called the legs. The term ‘trapezium,’ from which we got our word trapezoid has been in use in the English language since the 1500s and is from the Latin meaning ‘little table.’
Area (a) of a trapezium
1/2 x (sum of parallel sides) x perpendicular
Distance between the parallel sides
i.e.,
Where, l = b – a if b > a = a – b if a > b
And
Height (h) of the trapezium
Pathways Running across the middle of a rectangle:
X is the width of the path
Area of path= (l+b-x)x
perimeter= 2(l+b-2x)
Outer Pathways:
Area=(l+b+2x)2x
Perimeter=4(l+b+2x)
Inner Pathways:
Area=(l+b-2x)2x
Perimeter=4(l+b-2x)
SSC CGL Mathematics 2D Formulas & Basic Notes Complete Details
Cube
- s = side
- Volume: V = s^3
- Lateral surface area = 4a2
- Surface Area: S = 6s^2
- Diagonal (d) = s√3
Cuboid
- Volume of cuboid: length x breadth x width
- Total surface area = 2 ( lb + bh + hl)
Right Circular Cylinder
- Volume of Cylinder = π r^2 h
- Lateral Surface Area (LSA or CSA) = 2π r h
- Total Surface Area = TSA = 2 π r (r + h)
Right Circular Cone
- l^2 = r^2 + h^2
- Volume of cone = 1/3 π r^2 h
- Curved surface area: CSA= π r l
- Total surface area = TSA = πr(r + l )
Frustum of a Cone
- r = top radius, R = base radius,
- h = height, s = slant height
- Volume: V = π/ 3 (r^2 + rR + R^2)h
- Surface Area: S = πs(R + r) + πr^2 + πR^2
Sphere
- r = radius
- Volume: V = 4/3 πr^3
- Surface Area: S = 4π^2
Hemisphere
- Volume-Hemisphere = 2/3 π r^3
- Curved surface area(CSA) = 2 π r^2
- Total surface area = TSA = 3 π r^2
Prism
- Volume = Base area x height
- Lateral Surface area = perimeter of the base x height
Pyramid
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