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Chapter 20: Mensuration Exercise 20.3 Question: 1 The following figures are drawn on a squared paper. Count the number of squares enclosed by each figure and find its area, taking the area of each square as 1 cm2. Solution: (i) There are 16 complete squares in the given shape. Since, Area of one square = 1 cm2 Therefore, Area of this shape = 16 × 1 = 16 cm2 (ii) There are 36 complete squares in the given shape. Since, Area of one square = 1 cm2 Therefore, Area of 36 squares = 36 × 1 = 36 cm2 (iii) There are 15 complete and 6 half squares in the given shape. Since, Area of one square = 1 cm2 Therefore, Area of this shape = (15 + 6 × 12) = 18 cm2 (iv) There are 20 complete and 8 half squares in the given shape. Since, Area of one square = 1 cm2 Therefore, Area of this shape = (20 + 8 × 12) = 24 cm2 (v) There are 13 complete squares, 8 more than half squares and 7 less than half squares in the given shape. Area of one square = 1 cm2 Area of this shape = (13 + 8 × 1) = 21 cm2 (vi) There are 8 complete squares, 6 more than half squares and 4 less than half squares in the given shape. Area of one square = 1 cm2 Area of this shape = (8 + 6 × 1) = 14 cm2 Question: 2 On a squared paper, draw (i) a rectangle, (ii) a triangle, (iii) any irregular closed figure, Find approximate area of each by counting the number of squares complete, more than half and exactly half. Solution: (i) A rectangle: This contains 18 complete squares. If we assume that the area of one complete square is 1 cm2, Then the area o this rectangle will be 18 cm2. (ii) A triangle: This triangle contains 4 complete squares, 6 more than half squares and 6 less than half squares. If we assume that the area of one complete square is 1 cm2, Then the area of this shape = (4 + 6 x 1) = 10 cm2 (iii) Any irregular figure: This figure consists of 10 complete squares, 1 exactly half square, 7 more than half squares and 6 less than half squares. If we assume that the area of one complete square is 1 cm2, Then the area of this shape = (10 + 1 x12 + 7 x 1) = 17.5 cm2 Question: 3 Draw any circle on the graph paper, Count the squares and use them to estimate the area the area of the circular region. Solution: This circle on the squared paper consists of 21 complete squares, 15 more than half squares and 8 less than half squares. Let us assume that the area of 1 square is 1 cm2. If we neglect the less than half squares while approximating more than half square as equal to a complete square, we get: Area of this shape = (21 + 15) = 36 cm2 Question: 4 Using tracing paper and centimeter graph paper to compare the areas of the following pairs of figures: Solution: Using tracing paper, we traced both the figures on a graph paper. This figure contains 4 complete squares, 9 more than half squares and 9 less than half squares. Let us assume that the area of one square is 1 cm2 If we neglect the less than half squares and consider the area of more than half squares as equal to area of complete square, we get: Area of this shape = (4 + 9) = 13 cm2 This figure contains 8 complete squares, 11 more than half squares and 10 less than half squares. Let us assume that the area of one square is 1 cm2. If we neglect the less than half squares and consider the area of more than half squares as equal to area of complete square, we get: Area of this shape = (8 + 11) = 19 cm2 On comparing the areas of these two shapes, we get that the area of Fig. (ii) is more than that of Fig. (i).
The following figures are drawn on a squared paper. Count the number of squares enclosed by each figure and find its area, taking the area of each square as 1 cm2.
(i) There are 16 complete squares in the given shape.
Since, Area of one square = 1 cm2
Therefore, Area of this shape = 16 × 1 = 16 cm2
(ii) There are 36 complete squares in the given shape.
Therefore, Area of 36 squares = 36 × 1 = 36 cm2
(iii) There are 15 complete and 6 half squares in the given shape.
Therefore, Area of this shape = (15 + 6 × 12) = 18 cm2
(iv) There are 20 complete and 8 half squares in the given shape.
Therefore, Area of this shape = (20 + 8 × 12) = 24 cm2
(v) There are 13 complete squares, 8 more than half squares and 7 less than half squares in the given shape.
Area of one square = 1 cm2
Area of this shape = (13 + 8 × 1) = 21 cm2
(vi) There are 8 complete squares, 6 more than half squares and 4 less than half squares in the given shape.
Area of this shape = (8 + 6 × 1) = 14 cm2
On a squared paper, draw (i) a rectangle, (ii) a triangle, (iii) any irregular closed figure, Find approximate area of each by counting the number of squares complete, more than half and exactly half.
(i) A rectangle: This contains 18 complete squares.
If we assume that the area of one complete square is 1 cm2,
Then the area o this rectangle will be 18 cm2.
(ii) A triangle: This triangle contains 4 complete squares, 6 more than half squares and 6 less than half squares.
Then the area of this shape = (4 + 6 x 1) = 10 cm2
(iii) Any irregular figure: This figure consists of 10 complete squares, 1 exactly half square, 7 more than half squares and 6 less than half squares.
Then the area of this shape = (10 + 1 x12 + 7 x 1) = 17.5 cm2
This circle on the squared paper consists of 21 complete squares, 15 more than half squares and 8 less than half squares.
Let us assume that the area of 1 square is 1 cm2.
If we neglect the less than half squares while approximating more than half square as equal to a complete square, we get:
Area of this shape = (21 + 15) = 36 cm2
Using tracing paper and centimeter graph paper to compare the areas of the following pairs of figures:
Using tracing paper, we traced both the figures on a graph paper.
This figure contains 4 complete squares, 9 more than half squares and 9 less than half squares. Let us assume that the area of one square is 1 cm2
If we neglect the less than half squares and consider the area of more than half squares as equal to area of complete square, we get:
Area of this shape = (4 + 9) = 13 cm2
This figure contains 8 complete squares, 11 more than half squares and 10 less than half squares.
Let us assume that the area of one square is 1 cm2.
Area of this shape = (8 + 11) = 19 cm2
On comparing the areas of these two shapes, we get that the area of Fig. (ii) is more than that of Fig. (i).
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