CBSE Notes Class 7 Maths Chapter 9 Perimeter and Area
Chapter 9 of Class 7 Maths introduces the concepts of Perimeter and Area. Mensuration is the process or art of measuring, applied to anything that can be measured. In geometry, perimeter refers to the total boundary length of a closed figure, while area is the amount of surface covered by a shape. A planar region, which has two dimensions (length and breadth), is measured in terms of its area. These concepts are essential for solving practical problems like determining the length of fencing required or the amount of material needed for flooring.
1.0Triangle
Perimeter of a Triangle
Perimeter = Sum of Sides = a + b +c
Area of a Triangle:
Area =21× base × height
Area of an Equilateral Triangle:
Area =43a2,where (a) is the side length.
NOTE: ALSO WRITE h in equilateral Triangle.
Median/Altitude/Angle Bisector: For an equilateral triangle, the median (or altitude) is: Median =23a
Circumcircle and Incircle: If (R) is the radius of the circumcircle and (r) is the radius of the incircle: R = 2r
Perimeter of an Equilateral Triangle: Perimeter =3a
Area of an Isosceles Triangle: Area =4b4a2−b2
Height of an Isosceles Triangle: Height =a2−(4b2)
2.0Quadrilateral
Area of Any Quadrilateral: The area is the sum of the areas of two triangles formed by a diagonal.
If diagonals are inside the quadrilateral
Area =21× diagonal ×( Sum of the two perpendiculars )
A=21×d×(P1+P2)
If the diagonal falls outside the figure, then
Area of the quadrilateral =21× diagonal ×( difference of the perpendiculars )
Area =21×d×(P1−P2)
3.0Square
A square is a quadrilateral where:
All sides are equal: AB = BC = CD = DA = a
Diagonals are equal: AC = BD = d
Diagonals bisect each other at 90°, with a2=2d2
Perimeter of a Square:
Perimeter =4× side =4a
Area of a Square:
Area = side 2=a2
Area =2 diagonal =2d2
Diagonal of a square=2(sides)
4.0Rectangle
A rectangle is a quadrilateral whose,
Opposite sides equal and parallel: AB=CD=ℓ (length), AD = BC = b (breadth)
Equal diagonals that bisect each other: AC = BD = d
All angles ∠A=∠B=∠C=∠D=90∘
Diagonal relation:
d2=l2+b2
Area of a Rectangle:
Area = length × breadth =l×b
Perimeter of a Rectangle:
Perimeter =2 (length + breadth )=2(l+b)
5.0Parallelogram
A parallelogram is a quadrilateral with:
Opposite sides equal and parallel: AB = CD = b, AD = BC = a