The areas of Shapes F and G are equal. These two shapes are congruent right-angled triangles with identical dimensions. By comparing them side by side or overlaying them, it becomes clear that they occupy the same space. Their equality in area is also evident through their positions within the tangrRead more
The areas of Shapes F and G are equal. These two shapes are congruent right-angled triangles with identical dimensions. By comparing them side by side or overlaying them, it becomes clear that they occupy the same space. Their equality in area is also evident through their positions within the tangram, as they are symmetrical and evenly distributed within the overall square.
The area of Shape A is significantly larger than Shape G, being exactly four times as big. Shape A shares the same area as Shape B, and both are large right-angled triangles that form half of the total tangram square. On the other hand, Shape G is smaller and shares its area with Shape F. By compariRead more
The area of Shape A is significantly larger than Shape G, being exactly four times as big. Shape A shares the same area as Shape B, and both are large right-angled triangles that form half of the total tangram square. On the other hand, Shape G is smaller and shares its area with Shape F. By comparing dimensions or breaking Shape A into smaller segments, the fourfold difference in area becomes clear.
The big square formed by all seven tangram pieces has a total area equal to 8 times the area of Shape C. Shape D is twice the size of Shape C (2C), while Shapes A and B each have an area of 2C. Shapes F and G have an area equal to C, and together, they contribute 2C. Combining all the areas (2C fromRead more
The big square formed by all seven tangram pieces has a total area equal to 8 times the area of Shape C. Shape D is twice the size of Shape C (2C), while Shapes A and B each have an area of 2C. Shapes F and G have an area equal to C, and together, they contribute 2C. Combining all the areas (2C from A, B, D, and 2C from F and G), the total is 8C.
When the 7 tangram pieces are rearranged into a rectangle, the total area remains 8 times the area of Shape C. The dimensions of the rectangle may differ from the square, but the pieces are the same, so their combined area does not change. Each piece (A, B, C, D, E, F, and G) retains its original coRead more
When the 7 tangram pieces are rearranged into a rectangle, the total area remains 8 times the area of Shape C. The dimensions of the rectangle may differ from the square, but the pieces are the same, so their combined area does not change. Each piece (A, B, C, D, E, F, and G) retains its original contribution to the total, maintaining the overall area as 8C. This is a basic principle of geometry, where area is conserved.
The perimeters of the square and the rectangle formed from the tangram pieces are different. While the total area of both shapes is identical (8C), the perimeter depends on the dimensions of the shape. A square has equal-length sides, minimizing its perimeter for a given area. However, when rearrangRead more
The perimeters of the square and the rectangle formed from the tangram pieces are different. While the total area of both shapes is identical (8C), the perimeter depends on the dimensions of the shape. A square has equal-length sides, minimizing its perimeter for a given area. However, when rearranged into a rectangle, the longer and shorter sides increase the perimeter. This highlights how the arrangement of the same area affects the overall boundary length.
Squares are ideal for measuring area as they perfectly cover a surface without leaving gaps or overlaps. Circles and other shapes often leave spaces when packed, leading to less accurate measurements. The uniformity of square units ensures consistency and simplicity in calculations, making them theRead more
Squares are ideal for measuring area as they perfectly cover a surface without leaving gaps or overlaps. Circles and other shapes often leave spaces when packed, leading to less accurate measurements. The uniformity of square units ensures consistency and simplicity in calculations, making them the most practical choice for measuring diverse shapes and areas accurately.
Given the area of 24 square units, the rectangle with dimensions 1 × 24 has the greatest perimeter of 50 units due to its elongated shape. Conversely, the rectangle with dimensions 4 × 6 has the least perimeter of 20 units, as it is closer to a square. Generally, compact shapes like squares minimizeRead more
Given the area of 24 square units, the rectangle with dimensions 1 × 24 has the greatest perimeter of 50 units due to its elongated shape. Conversely, the rectangle with dimensions 4 × 6 has the least perimeter of 20 units, as it is closer to a square. Generally, compact shapes like squares minimize perimeter for a given area, while elongated shapes maximize it.
For an area of 32 square cm, the rectangle with dimensions 1 × 32 has the greatest perimeter of 66 cm, while the one with 4 × 8 has the least perimeter of 24 cm. Compact shapes, such as squares or near-squares, minimize perimeter because the sides are balanced. Elongated shapes, with one very long aRead more
For an area of 32 square cm, the rectangle with dimensions 1 × 32 has the greatest perimeter of 66 cm, while the one with 4 × 8 has the least perimeter of 24 cm. Compact shapes, such as squares or near-squares, minimize perimeter because the sides are balanced. Elongated shapes, with one very long and one short side, maximize perimeter. Thus, the more balanced the dimensions, the smaller the perimeter for a fixed area.
A triangle is a three-sided polygon with three edges and three vertices, forming the simplest closed figure in geometry. Its area represents the space enclosed by its three sides. The formula for the area of a triangle is half the product of its base and height. Mathematically, it is given as (baseRead more
A triangle is a three-sided polygon with three edges and three vertices, forming the simplest closed figure in geometry. Its area represents the space enclosed by its three sides. The formula for the area of a triangle is half the product of its base and height. Mathematically, it is given as (base × height) ÷ 2. This method ensures accurate calculation of the triangular region, irrespective of the triangle’s type or orientation.
When a rectangle is divided by its diagonal, two identical triangles are formed. These triangles can be checked for congruence by overlapping them, and they align perfectly. As the diagonal divides the rectangle into two equal parts, the area of each triangle is exactly half of the rectangle's area.Read more
When a rectangle is divided by its diagonal, two identical triangles are formed. These triangles can be checked for congruence by overlapping them, and they align perfectly. As the diagonal divides the rectangle into two equal parts, the area of each triangle is exactly half of the rectangle’s area. This observation remains true for any rectangle or square, irrespective of its size.
Which shape has more area: Shape F or G? Give reasons for your answer.
The areas of Shapes F and G are equal. These two shapes are congruent right-angled triangles with identical dimensions. By comparing them side by side or overlaying them, it becomes clear that they occupy the same space. Their equality in area is also evident through their positions within the tangrRead more
The areas of Shapes F and G are equal. These two shapes are congruent right-angled triangles with identical dimensions. By comparing them side by side or overlaying them, it becomes clear that they occupy the same space. Their equality in area is also evident through their positions within the tangram, as they are symmetrical and evenly distributed within the overall square.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
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What is the area of Shape A as compared to Shape G? Is it twice as big? Four times as big?
The area of Shape A is significantly larger than Shape G, being exactly four times as big. Shape A shares the same area as Shape B, and both are large right-angled triangles that form half of the total tangram square. On the other hand, Shape G is smaller and shares its area with Shape F. By compariRead more
The area of Shape A is significantly larger than Shape G, being exactly four times as big. Shape A shares the same area as Shape B, and both are large right-angled triangles that form half of the total tangram square. On the other hand, Shape G is smaller and shares its area with Shape F. By comparing dimensions or breaking Shape A into smaller segments, the fourfold difference in area becomes clear.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
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Can you now figure out the area of the big square formed with all seven pieces in terms of the area of Shape C?
The big square formed by all seven tangram pieces has a total area equal to 8 times the area of Shape C. Shape D is twice the size of Shape C (2C), while Shapes A and B each have an area of 2C. Shapes F and G have an area equal to C, and together, they contribute 2C. Combining all the areas (2C fromRead more
The big square formed by all seven tangram pieces has a total area equal to 8 times the area of Shape C. Shape D is twice the size of Shape C (2C), while Shapes A and B each have an area of 2C. Shapes F and G have an area equal to C, and together, they contribute 2C. Combining all the areas (2C from A, B, D, and 2C from F and G), the total is 8C.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
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Arrange these 7 pieces to form a rectangle. What will be the area of this rectangle in terms of the area of Shape C? Give reasons for your answer.
When the 7 tangram pieces are rearranged into a rectangle, the total area remains 8 times the area of Shape C. The dimensions of the rectangle may differ from the square, but the pieces are the same, so their combined area does not change. Each piece (A, B, C, D, E, F, and G) retains its original coRead more
When the 7 tangram pieces are rearranged into a rectangle, the total area remains 8 times the area of Shape C. The dimensions of the rectangle may differ from the square, but the pieces are the same, so their combined area does not change. Each piece (A, B, C, D, E, F, and G) retains its original contribution to the total, maintaining the overall area as 8C. This is a basic principle of geometry, where area is conserved.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
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Are the perimeters of the square and the rectangle formed from these 7 pieces different or the same? Give an explanation for your answer.
The perimeters of the square and the rectangle formed from the tangram pieces are different. While the total area of both shapes is identical (8C), the perimeter depends on the dimensions of the shape. A square has equal-length sides, minimizing its perimeter for a given area. However, when rearrangRead more
The perimeters of the square and the rectangle formed from the tangram pieces are different. While the total area of both shapes is identical (8C), the perimeter depends on the dimensions of the shape. A square has equal-length sides, minimizing its perimeter for a given area. However, when rearranged into a rectangle, the longer and shorter sides increase the perimeter. This highlights how the arrangement of the same area affects the overall boundary length.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions-class-6-maths-ganita-prakash-chapter-6/
Why is area generally measured using squares?
Squares are ideal for measuring area as they perfectly cover a surface without leaving gaps or overlaps. Circles and other shapes often leave spaces when packed, leading to less accurate measurements. The uniformity of square units ensures consistency and simplicity in calculations, making them theRead more
Squares are ideal for measuring area as they perfectly cover a surface without leaving gaps or overlaps. Circles and other shapes often leave spaces when packed, leading to less accurate measurements. The uniformity of square units ensures consistency and simplicity in calculations, making them the most practical choice for measuring diverse shapes and areas accurately.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions-class-6-maths-ganita-prakash-chapter-6/
Which rectangle has the greatest perimeter? b. Which rectangle has the least perimeter?
Given the area of 24 square units, the rectangle with dimensions 1 × 24 has the greatest perimeter of 50 units due to its elongated shape. Conversely, the rectangle with dimensions 4 × 6 has the least perimeter of 20 units, as it is closer to a square. Generally, compact shapes like squares minimizeRead more
Given the area of 24 square units, the rectangle with dimensions 1 × 24 has the greatest perimeter of 50 units due to its elongated shape. Conversely, the rectangle with dimensions 4 × 6 has the least perimeter of 20 units, as it is closer to a square. Generally, compact shapes like squares minimize perimeter for a given area, while elongated shapes maximize it.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
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If you take a rectangle of area 32 sq cm, what will your answers be? Given any area, is it possible to predict the shape of the rectangle with the greatest perimeter as well as the least perimeter? Give examples and reasons for your answer.
For an area of 32 square cm, the rectangle with dimensions 1 × 32 has the greatest perimeter of 66 cm, while the one with 4 × 8 has the least perimeter of 24 cm. Compact shapes, such as squares or near-squares, minimize perimeter because the sides are balanced. Elongated shapes, with one very long aRead more
For an area of 32 square cm, the rectangle with dimensions 1 × 32 has the greatest perimeter of 66 cm, while the one with 4 × 8 has the least perimeter of 24 cm. Compact shapes, such as squares or near-squares, minimize perimeter because the sides are balanced. Elongated shapes, with one very long and one short side, maximize perimeter. Thus, the more balanced the dimensions, the smaller the perimeter for a fixed area.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
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What do you mean by Triangle? Define Area of a Triangle.
A triangle is a three-sided polygon with three edges and three vertices, forming the simplest closed figure in geometry. Its area represents the space enclosed by its three sides. The formula for the area of a triangle is half the product of its base and height. Mathematically, it is given as (baseRead more
A triangle is a three-sided polygon with three edges and three vertices, forming the simplest closed figure in geometry. Its area represents the space enclosed by its three sides. The formula for the area of a triangle is half the product of its base and height. Mathematically, it is given as (base × height) ÷ 2. This method ensures accurate calculation of the triangular region, irrespective of the triangle’s type or orientation.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions-class-6-maths-ganita-prakash-chapter-6/
Check whether the two triangles overlap each other exactly. Do they have the same area?
When a rectangle is divided by its diagonal, two identical triangles are formed. These triangles can be checked for congruence by overlapping them, and they align perfectly. As the diagonal divides the rectangle into two equal parts, the area of each triangle is exactly half of the rectangle's area.Read more
When a rectangle is divided by its diagonal, two identical triangles are formed. These triangles can be checked for congruence by overlapping them, and they align perfectly. As the diagonal divides the rectangle into two equal parts, the area of each triangle is exactly half of the rectangle’s area. This observation remains true for any rectangle or square, irrespective of its size.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions-class-6-maths-ganita-prakash-chapter-6/