Perimeter and Area: Maths Class 7 Chapter-11

Key Features of NCERT Material for Class 7 Maths Chapter 11 –  Perimeter and Area

Quick revision notes

In Chapter 10 of Class 7 NCERT book: you must have learnt about Practical Geometry. In chapter 11:  you will learn about various forms of Perimeter and Area.

Perimeter

• Perimeter is the total length or total distance covered along the boundary of a closed shape.

Area

• The area is the total amount of surface enclosed by a closed figure.

The perimeter of Square and Rectangle

• Perimeter of a square = a + a + a + a = 4a, where a is the length of each side.

• Perimeter of a rectangle = l + l + b + b = 2(l + b), where l and b are length and breadth, respectively.

Area of Square & Rectangle

Area of square = 4a²

Area of rectangle = Length(l) × Breadth(b) = l×b

Area of a Parallelogram

• Area of parallelogram ABCD = (base×height)

The perimeter of a regular polygon = number of sides × length of one side

The perimeter of a square = 4 × side

Perimeter of rectangle = 2 × (l + b)

(where l and b denote the length and breadth respectively of the rectangle)

Area of a square = side × side

Area of a rectangle = l × b

Triangles as Parts of Rectangles

The sum of the areas of the two triangles, into which a diagonal of a rectangle divides the rectangle, is the same as the area of the rectangle. Also, both the triangles are equal in area.

Generalising for Other Congruent Parts of Rectangles

If we divide a rectangle into two congruent parts so that the area of one part is equal to the area of the other part, then

area of each congruent part = (the area of the rectangle)

Area of parallelogram = base × corresponding height (altitude)

Conversion of Units

1cm =10 mm

1 cm2 = 100 mm2

1 m2 = 100 × 100 = 10,000 cm2

1 km2 = 1000 × 1000 = 1,000,000 m2

1 hectare = 10,000 m2

Perimeter of square = 4 × side

Perimeter of Rectangle = 2 × (length + breadth)

Perimeter of triangle = sum of all sides of triangle = a + b + c

Area of square = side × side = (side)2

Area of Rectangle = Length × Breadth = l × b

Area of Triangle = × Base × Height (Altitude)

Area of a parallelogram = Base × Height

The distance around a circular region is known as its circumference.

Circumference of a circle = πd = π(2r) = 2πr. where d is diameter and r is the radius.

Area of a circle = πr2

π = or 3.14 (approximately).