NCERT Solutions for Class 6th Maths Chapter 6 Straight and diagonal units · Perimeter of a regular polygon — In-text Questions
Book page 135 Updated on2026-09-19
Q1.
Write the perimeters of the figures below in terms of straight and diagonal units.
The four figures drawn on the dot grid. Every side runs either along the grid (a straight unit) or from corner to corner of one square (a diagonal unit).
Answer
Walk once round each figure and count the two kinds of steps separately: s for a straight (grid) unit and d for a diagonal unit.
The four figures on the dot grid. Every side is either a straight unit (along the grid) or a diagonal unit (corner to corner of one square).
Figure
Straight units counted
Diagonal units counted
Perimeter
a. (the “F”)
3 + 1 + 1 + 3 = 8
1 + 1 = 2
8s + 2d
b. (the “heart”)
1 + 2 + 1 = 4
6
4s + 6d
c. (the “U”)
3 + 2 + 1 + 3 + 1 + 2 = 12
6
12s + 6d
d. (the “N”)
4 + 1 + 3 + 1 + 4 + 1 + 3 + 1 = 18
3 + 3 = 6
18s + 6d
Why we do not just add s and d: they are two different lengths. Writing 8s + 2d keeps the answer exact. If you want an approximate number, use d ≈ 1.4s — for figure a that gives 8 + 2 × 1.4 ≈ 10.8 units.
Q2.
What is a similarity between a square and an equilateral triangle?
Answer
Both are regular polygons — closed figures in which all sides are equal and all angles are equal.
Equilateral triangle
Square
Number of sides
3
4
All sides equal?
Yes
Yes
All angles equal?
Yes (60° each)
Yes (90° each)
Perimeter
3 × side
4 × side
Because of this, in both figures the perimeter can be found by one multiplication instead of adding the sides one by one.
Perimeter of a regular polygon = number of sides × length of a side