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Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_30.1

Study Notes on 2D Mensuration

Mathematics is an equally important section for  REETMPTET & DSSSB Exams and has even more abundant importance in some other exams conducted by central or state govt. Generally, there are questions asked related to basic concepts and formulas of the Mensuration.

To let you make the most of Mathematics section, we are providing important facts related to the 2D Mensuration. At least 3-4 questions are asked from mensuration topic in most of the teaching exams. We wish you all the best of luck to come over the fear of the Mathematics section.

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Rectangle

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_40.1

(a) Its diagonals are equal and bisect each other

(b) Area = L×B

(c) Diagonal d= Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_50.1

(d) (i) Area of a path inside a rectangular field:

Area of Path= 2x(l+b-2x)

(ii) Perimeter (p)= inner p+ outer p

= 2(l+b)+2(l+b-4x)

= 4(l+b-2x)

(e) Room as a Rectangular figure:

Area of 4 walls of a room= perimeter × height

= 2(l+b)×h

(f) Area of roof and 4 walls = 2H (L+B)+LB

Example: A rectangular piece is 40cm long and 30m wide from its four corners, quadrants of radii 3.5m have been cut. The area of remaining part is:

Sol. Area of Rectangle – 4 × area of quarter circle

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_60.1

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Square

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_70.1

(a) Area = a² or ×(diagonal)²

(b) Perimeter = 4a

(c) Diagonal =Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_80.1

(d) Area of path inside square = 4d(x-d)

X= length of square, d= length of path

(e) Area of path outside square = 4d (x+d)

(f) Area of path midway square = d(2x-d)

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_90.1

Example: If each side of square park is increased by 35%. Find the percentage change in its area?

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_100.1

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Parallelogram

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_110.1

(a) Area = base × height

(b) Perimeter= 2(a + b)

(c) d₁²+ d₂²= 2(a²+b²)

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_120.1

Example: A parallelogram PQRS has side PQ = 36cm and PS = 24cm. The distance between the sides PQ and RS is 16cm. Find the distance between the side PS and RQ.

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_130.1

Mathematics Study Notes For All Teaching Exams

Rhombus:

It is a quadrilateral whose all four sides are equal. Diagonal bisect each other at 90°

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_140.1

Example: The perimeter of Rhombus is 60cm and the measure of an angle is 60° then the area is:

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_150.1

Trapezium

It is a quadrilateral, whose any two opposite sides are parallel.

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_160.1

Practice Mensuration 2D Quiz Here for CTET Exam 

Triangle

A triangle is a polygon with three edges and three vertices.

Types of triangles:

  • Scalene Triangle: A scalene triangle has all its sides of different lengths.

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_170.1

Example: The ratio of sides of a triangle is 4:5:6. If perimeter of triangle is 90 cm then the Area of triangle is

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_180.1

  • Isosceles Triangle: An Isosceles triangle is a triangle with two equal sides also their opposite angles are equal.

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_190.1

  • Right angle triangle: It is a triangle with an angle of 90° The sides a, b and c of such a triangle satisfy the pythagoras theorem.

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_200.1

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_210.1

  • Equilateral triangle: It is a triangle whose all sides and angle are equal.

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_220.1

  • ∠A=∠B=∠C= 60°
  • If P₁, P₂, and P₃ are perpendicular lengths from any interior point (O) of an equilateral ∆ ABC to all its three sides respectively, then:

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_230.1

Example: Each side of an equilateral triangle is 16 cm. the area of triangle is:

Mensuration – 2D : : Download Mathematics Study Notes Free PDF For REET/UTET Exam_240.1

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