NCERT Solutions for Class 6th Maths Chapter 6 Estimating area by counting squares — In-text Questions
Book page 140 Updated on2026-09-19
Q1.
Look at the figures below and guess which one of them has a larger area.
The two closed shapes printed on page 140.
Answer
By eye it is almost impossible to say — and that is exactly the point of the question. Shape b has sharp spikes that make it look bigger, while shape a is smooth and rounded.
The honest way to decide: trace each shape on transparent paper, place it on squared paper and count the squares using the four rules:
one full square = 1 sq unit;
more than half a square = 1 sq unit;
exactly half a square = ½ sq unit;
less than half a square = ignore it.
When this is done carefully, the smooth shape a turns out to cover slightly more squares than the spiky shape b — the spikes of b are thin, so they add very little region.
Why our eyes get fooled: we tend to judge by how far a figure spreads out, not by how much region it actually fills. A long thin spike adds a lot of boundary (perimeter) but very little area.
Q2.
Find the area of the following figures.
The same four figures on the dot grid, where four neighbouring dots enclose one square unit.
Answer
Each figure is drawn on a dot grid where four neighbouring dots make one square unit. Break each figure into rectangles, squares and half-squares (right triangles) and add.
The four figures again. Slanting sides always cut a unit square into two equal halves, each of area ½ sq unit.
Figure
How it splits up
Area
a. (the “F”)
2 full squares + 4 half-squares
4 sq units
b. (the “heart”)
6 full squares + 6 half-squares
9 sq units
c. (the “U”)
7 full squares + 6 half-squares
10 sq units
d. (the “N”)
two 1 × 4 bars + a slanting bar
11 sq units
Answers: 4, 9, 10 and 11 square units.
Tip for the “N”: the two upright bars are 1 × 4 = 4 and 1 × 4 = 4 squares. The slanting bar covers 3 more squares, giving 4 + 4 + 3 = 11 sq units.