The square's perimeter is 4 × side. After folding, two rectangles are formed with lengths equal to half the square's side. The total perimeter of both rectangles is 6 × side, which is 1.5 times the square's perimeter. Thus, the correct option is (c): The perimeters of both rectangles added togetherRead more
The square’s perimeter is 4 × side. After folding, two rectangles are formed with lengths equal to half the square’s side. The total perimeter of both rectangles is 6 × side, which is 1.5 times the square’s perimeter.
Thus, the correct option is (c): The perimeters of both rectangles added together are always 1.5 times the perimeter of the square.
Among the tangram pieces, Shapes C and E have the same area because they are identical in size and shape. Similarly, Shapes A and B share equal areas, as they are congruent triangles. Shapes F and G are also equal in area. However, Shape D is larger and cannot be paired with another shape of the samRead more
Among the tangram pieces, Shapes C and E have the same area because they are identical in size and shape. Similarly, Shapes A and B share equal areas, as they are congruent triangles. Shapes F and G are also equal in area. However, Shape D is larger and cannot be paired with another shape of the same area. This comparison is evident by overlaying the shapes on each other.
Shape D is twice as large as Shape C. By placing the pieces together, we see that Shape D can be entirely formed by combining Shapes C and E. This indicates that Shapes C and E are equal in area, and their combined areas equal that of Shape D. Thus, Shape D represents the total area of two smaller iRead more
Shape D is twice as large as Shape C. By placing the pieces together, we see that Shape D can be entirely formed by combining Shapes C and E. This indicates that Shapes C and E are equal in area, and their combined areas equal that of Shape D. Thus, Shape D represents the total area of two smaller identical pieces, making its size double that of a single Shape C or E.
Shape D is larger than Shape F in terms of area. Shape D is made up of the combined areas of Shapes C and E, making it twice the size of Shape C. On the other hand, Shape F has an area equal to Shape C. Therefore, the area of Shape D is two times that of Shape F, as it is composed of more identicalRead more
Shape D is larger than Shape F in terms of area. Shape D is made up of the combined areas of Shapes C and E, making it twice the size of Shape C. On the other hand, Shape F has an area equal to Shape C. Therefore, the area of Shape D is two times that of Shape F, as it is composed of more identical smaller sections.
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.
A square piece of paper is folded in half. The square is then cut into two rectangles along the fold. Regardless of the size of the square, one of the following statements is always true. Which statement is true here? a. The area of each rectangle is larger than the area of the square. b. The perimeter of the square is greater than the perimeters of both the rectangles added together. c. The perimeters of both the rectangles added together is always 1 1/2 times the perimeter of the square. d. The area of the square is always three times as large as the areas of both rectangles added together.
The square's perimeter is 4 × side. After folding, two rectangles are formed with lengths equal to half the square's side. The total perimeter of both rectangles is 6 × side, which is 1.5 times the square's perimeter. Thus, the correct option is (c): The perimeters of both rectangles added togetherRead more
The square’s perimeter is 4 × side. After folding, two rectangles are formed with lengths equal to half the square’s side. The total perimeter of both rectangles is 6 × side, which is 1.5 times the square’s perimeter.
Thus, the correct option is (c): The perimeters of both rectangles added together are always 1.5 times the perimeter of the square.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
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Explore and figure out how many pieces have the same area.
Among the tangram pieces, Shapes C and E have the same area because they are identical in size and shape. Similarly, Shapes A and B share equal areas, as they are congruent triangles. Shapes F and G are also equal in area. However, Shape D is larger and cannot be paired with another shape of the samRead more
Among the tangram pieces, Shapes C and E have the same area because they are identical in size and shape. Similarly, Shapes A and B share equal areas, as they are congruent triangles. Shapes F and G are also equal in area. However, Shape D is larger and cannot be paired with another shape of the same area. This comparison is evident by overlaying the shapes on each other.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
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How many times bigger is Shape D as compared to Shape C? What is the relationship between Shapes C, D, and E?
Shape D is twice as large as Shape C. By placing the pieces together, we see that Shape D can be entirely formed by combining Shapes C and E. This indicates that Shapes C and E are equal in area, and their combined areas equal that of Shape D. Thus, Shape D represents the total area of two smaller iRead more
Shape D is twice as large as Shape C. By placing the pieces together, we see that Shape D can be entirely formed by combining Shapes C and E. This indicates that Shapes C and E are equal in area, and their combined areas equal that of Shape D. Thus, Shape D represents the total area of two smaller identical pieces, making its size double that of a single Shape C or E.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
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Which shape has more area: Shape D or F? Give reasons for your answer.
Shape D is larger than Shape F in terms of area. Shape D is made up of the combined areas of Shapes C and E, making it twice the size of Shape C. On the other hand, Shape F has an area equal to Shape C. Therefore, the area of Shape D is two times that of Shape F, as it is composed of more identicalRead more
Shape D is larger than Shape F in terms of area. Shape D is made up of the combined areas of Shapes C and E, making it twice the size of Shape C. On the other hand, Shape F has an area equal to Shape C. Therefore, the area of Shape D is two times that of Shape F, as it is composed of more identical smaller sections.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
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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/