GSEB Class 6 Maths Solutions Chapter 10 Mensuration Exercise 10.2

Question 1. Find the area of the following figures by counting squares
Answer:
(a) Number of full squares = 9
Area of the figure = \( 9 \times 1 \) sq. unit = 9 sq. units.

(b) Number of full squares = 5
Area of the figure = \( 5 \times 1 \) sq. unit = 5 sq. units.

(c) Number of full squares = 2
Number of half squares = 4
Area covered by the figure = \( (2 \times 1) + (\frac { 1 }{ 2 } \times 4) \) sq. unit
\( = 2 + 2 \) sq. units
\( = 4 \) sq. units.

(d) Number of full squares = 8
Area covered by the figure = \( 8 \times 1 \) sq. unit = 8 sq. units.

(e) Number of full squares = 10
Area covered by the figure = \( 10 \times 1 \) sq. unit = 10 sq. units.

(f) Number of full squares = 2
Number of half squares = 4
Area of the figure = \( (2 \times 1) \) sq. unit \( + (\frac { 1 }{ 2 } \times 4) \) sq. unit
\( = 2 \) sq. units \( + 2 \) sq. units
\( = 4 \) sq. units.

(g) Number of full squares = 4
Number of half squares = 4
Area of the figure = \( (4 \times 1) \) sq. unit \( + (\frac { 1 }{ 2 } \times 4) \) sq. unit
\( = 4 \) sq. units \( + 2 \) sq. units
\( = 6 \) sq. units.

(h) Number of full squares = 5
Area of the figure = \( 5 \times 1 \) sq. unit = 5 sq. units.

(j) Number of full squares = 2
Number of half squares = 4
Area of figure = \( (2 \times 1) \) sq. unit \( + (\frac { 1 }{ 2 } \times 4) \) sq. unit
\( = 2 \) sq. units \( + 2 \) sq. units
\( = 4 \) sq. units.

(k) Number of full squares = 4
Number of half squares = 2
Area of the figure = \( (4 \times 1) \) sq. unit \( + (\frac { 1 }{ 2 } \times 2) \) sq. unit
\( = 4 \) sq. units \( + 1 \) sq. unit
\( = 5 \) sq. units.

(l) Number of full squares = 4
Number of more than half squares = 3
Number of half squares = 2
Area of the figure = \( (4 \times 1) \) sq. unit \( + (3 \times 1) \) sq. unit \( + (\frac { 1 }{ 2 } \times 2) \) sq. unit
\( = 4 \) sq. units \( + 3 \) sq. units \( + 1 \) sq. unit
\( = 8 \) sq. units.

(m) Number of full squares = 6
Number of more than half squares = 8
Number of half squares = 0
Area covered by the figure = \( (6 \times 1) \) sq. unit \( + (8 \times 1) \) sq. unit
\( = 6 \) sq. units \( + 8 \) sq. units
\( = 14 \) sq. units.

(n) Number of full squares = 9
Number of more than half squares = 9
Area of the figure = \( (9 \times 1) \) sq. unit \( + (9 \times 1) \) sq. unit
\( = 9 \) sq. units \( + 9 \) sq. units
\( = 18 \) sq. units.
In simple words: To find the area of shapes on a grid, you need to count how many full squares they cover (each counts as 1 unit), how many squares are more than half covered (each also counts as 1 unit), and how many are exactly half covered (each counts as 0.5 units). Then, just add all these calculated values together to get the total area for each figure.

Exam Tip: For problems involving area by counting squares, meticulously categorize each square part (full, half, more than half) and apply the correct counting value to each before summing them up. Pay close attention to distinguishing between half and more-than-half squares.