NCERT Solutions Ganita Prakash Chapter 6 Straight and diagonal units · Perimeter of a regular polygon — In-text Questions
Book page 135 Updated on2026-09-05
Q1.
Write the perimeters of the figures below in terms of straight and diagonal units.
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