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NCERT Solutions for Class 5th Maths Chapter 11 Perimeter = 2 × Length + 2 × Breadth, and what happens when all sides are equal — From Rectangle to Square

Book page 151 Updated on2026-09-19

Q1.
What will happen if all the sides of a rectangle are equal, that is, the case of square?
Answer

The rectangle becomes a square, and both formulas get shorter.

  1. Start from the rectangle. Area = Length × Breadth, and Perimeter = 2 × Length + 2 × Breadth.
  2. Make all four sides equal. Now the breadth is the same as the length.
  3. Put “length” in place of “breadth”. Area becomes Length × Length. Perimeter becomes Length + Length + Length + Length, that is 4 × Length.
Rectangle
Area = Length × Breadth
Perimeter = 2 × Length + 2 × Breadth

Square
Area = Length × Length
Perimeter = 4 × Length
Why the shorter rules are allowed: A square is not a different kind of shape — it is a rectangle whose four sides happen to be equal. So every rule for a rectangle still works. We can just write it more simply, because there is only one measurement to remember instead of two.
Also true for the 6 cm × 4 cm rectangle on this page: Area = 6 × 4 = 24 square cm, and Perimeter = 2 × 6 + 2 × 4 = 12 + 8 = 20 cm.
Q2.
Let us think about a square whose sides are 5 units long. (Find its area and its perimeter.)
Answer

Area = 25 square cm. Perimeter = 20 cm.

A square of side 5Area = 5 × 5 = 25 square cmPerimeter = 4 × 5 = 20 cm
  1. Draw the square on a grid. 5 squares across and 5 squares down.
  2. Find the area. Each row has 5 unit squares and there are 5 rows, so 5 × 5 = 25 unit squares.
  3. Find the perimeter. Walk round the four sides: 5 + 5 + 5 + 5, which is 4 × 5 = 20.
  4. Write the units. Area is measured in square cm; perimeter is measured in cm.
Area of square = Length × Length
Area = 5 × 5
Area = 25 square cm

Perimeter of square = Length + Length + Length + Length
Perimeter = 4 × Length = 4 × 5
Perimeter = 20 cm
Why area and perimeter use different units: Perimeter is a length — a piece of string you could pull straight, so it is measured in cm. Area is a covering — a number of little 1 cm squares, so it is measured in square cm. Never write “25 cm” for an area, and never write “20 square cm” for a perimeter.
Check it yourself: Count the squares in the picture, five rows of five. You will reach 25. Now count the little edges round the outside — five on each side, so 20 in all.
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