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Page 1 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 cm 2 . (Fig. 20.25). Solution: (i) The given shape has 16 complete squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 16 × 1 = 16 cm 2 (ii) The given shape has 36 complete squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 36 × 1 = 36 cm 2 (iii) The given shape has 15 complete and 6 half squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 15 + 6 × 12 = 18 cm 2 (iv) The given shape has 20 complete and 8 half squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 20 + 8 × 12 = 24 cm 2 (v) The given shape has 13 complete, 8 more than half and 7 less than half squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 13 + 8 × 1 = 21 cm 2 (vi) The given shape has 8 complete, 6 more than half and 4 less than half squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 8 + 6 × 1 = 14 cm 2 2. On a squared paper, draw (i) a rectangle, (ii) a triangle (iii) any irregular closed figure. Find the approximate area of each by counting the number of squares complete, more than half and exactly half. Page 2 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 cm 2 . (Fig. 20.25). Solution: (i) The given shape has 16 complete squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 16 × 1 = 16 cm 2 (ii) The given shape has 36 complete squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 36 × 1 = 36 cm 2 (iii) The given shape has 15 complete and 6 half squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 15 + 6 × 12 = 18 cm 2 (iv) The given shape has 20 complete and 8 half squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 20 + 8 × 12 = 24 cm 2 (v) The given shape has 13 complete, 8 more than half and 7 less than half squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 13 + 8 × 1 = 21 cm 2 (vi) The given shape has 8 complete, 6 more than half and 4 less than half squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 8 + 6 × 1 = 14 cm 2 2. On a squared paper, draw (i) a rectangle, (ii) a triangle (iii) any irregular closed figure. Find the approximate area of each by counting the number of squares complete, more than half and exactly half. Solution: (i) A rectangle The given shape has 18 complete squares Assume that area of one square = 1 cm 2 So the area of the rectangle = 18 × 1 = 18 cm 2 (ii) A triangle The given shape has 4 complete, 6 more than half and 6 less than half squares. Assume that area of one square = 1 cm 2 So the area of the square = 4 + 6 × 1 = 10 cm 2 (iii) Any irregular figure The given shape has 10 complete, 1 exactly half, 7 more than half and 6 less than half squares. Assume that area of one square = 1 cm 2 So the area of the shape = 10 + 1 × 12 + 7 × 1 = 17.5 cm 2 Page 3 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 cm 2 . (Fig. 20.25). Solution: (i) The given shape has 16 complete squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 16 × 1 = 16 cm 2 (ii) The given shape has 36 complete squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 36 × 1 = 36 cm 2 (iii) The given shape has 15 complete and 6 half squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 15 + 6 × 12 = 18 cm 2 (iv) The given shape has 20 complete and 8 half squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 20 + 8 × 12 = 24 cm 2 (v) The given shape has 13 complete, 8 more than half and 7 less than half squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 13 + 8 × 1 = 21 cm 2 (vi) The given shape has 8 complete, 6 more than half and 4 less than half squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 8 + 6 × 1 = 14 cm 2 2. On a squared paper, draw (i) a rectangle, (ii) a triangle (iii) any irregular closed figure. Find the approximate area of each by counting the number of squares complete, more than half and exactly half. Solution: (i) A rectangle The given shape has 18 complete squares Assume that area of one square = 1 cm 2 So the area of the rectangle = 18 × 1 = 18 cm 2 (ii) A triangle The given shape has 4 complete, 6 more than half and 6 less than half squares. Assume that area of one square = 1 cm 2 So the area of the square = 4 + 6 × 1 = 10 cm 2 (iii) Any irregular figure The given shape has 10 complete, 1 exactly half, 7 more than half and 6 less than half squares. Assume that area of one square = 1 cm 2 So the area of the shape = 10 + 1 × 12 + 7 × 1 = 17.5 cm 2 3. Draw any circle on the graph paper. Count the squares and use them to estimate the area of the circular region. Solution: The given circles has 21 complete, 15 more than half and 8 less than half squares. Assume that area of one square = 1 cm 2 By neglecting less than half squares, we get Area of the circle = 21 + 15 = 36 cm 2 4. Use tracing paper and centimetre graph paper to compare the areas of the following pairs of figures: Solution: With the help of tracing paper trace both the figures on a graph Figure (i) has 4 complete, 9 more than half and 9 less than half squares. Assume that area of one square = 1 cm 2 By neglecting less than half squares, we get Area of the shape = 4 + 9 = 13 cm 2 Figure (ii) has 8 complete, 11 more than half and 10 less than half squares. Assume that area of one square = 1 cm 2 Page 4 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 cm 2 . (Fig. 20.25). Solution: (i) The given shape has 16 complete squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 16 × 1 = 16 cm 2 (ii) The given shape has 36 complete squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 36 × 1 = 36 cm 2 (iii) The given shape has 15 complete and 6 half squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 15 + 6 × 12 = 18 cm 2 (iv) The given shape has 20 complete and 8 half squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 20 + 8 × 12 = 24 cm 2 (v) The given shape has 13 complete, 8 more than half and 7 less than half squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 13 + 8 × 1 = 21 cm 2 (vi) The given shape has 8 complete, 6 more than half and 4 less than half squares. It is given that area of one square = 1 cm 2 So the area of the given shape = 8 + 6 × 1 = 14 cm 2 2. On a squared paper, draw (i) a rectangle, (ii) a triangle (iii) any irregular closed figure. Find the approximate area of each by counting the number of squares complete, more than half and exactly half. Solution: (i) A rectangle The given shape has 18 complete squares Assume that area of one square = 1 cm 2 So the area of the rectangle = 18 × 1 = 18 cm 2 (ii) A triangle The given shape has 4 complete, 6 more than half and 6 less than half squares. Assume that area of one square = 1 cm 2 So the area of the square = 4 + 6 × 1 = 10 cm 2 (iii) Any irregular figure The given shape has 10 complete, 1 exactly half, 7 more than half and 6 less than half squares. Assume that area of one square = 1 cm 2 So the area of the shape = 10 + 1 × 12 + 7 × 1 = 17.5 cm 2 3. Draw any circle on the graph paper. Count the squares and use them to estimate the area of the circular region. Solution: The given circles has 21 complete, 15 more than half and 8 less than half squares. Assume that area of one square = 1 cm 2 By neglecting less than half squares, we get Area of the circle = 21 + 15 = 36 cm 2 4. Use tracing paper and centimetre graph paper to compare the areas of the following pairs of figures: Solution: With the help of tracing paper trace both the figures on a graph Figure (i) has 4 complete, 9 more than half and 9 less than half squares. Assume that area of one square = 1 cm 2 By neglecting less than half squares, we get Area of the shape = 4 + 9 = 13 cm 2 Figure (ii) has 8 complete, 11 more than half and 10 less than half squares. Assume that area of one square = 1 cm 2 By neglecting less than half squares, we get Area of the shape = 8 + 11 = 19 cm 2 By comparing the areas of both the shapes, we know that the figure (ii) has area greater than that of figure (i).Read More
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