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Shapes and Designs - Tangrams

Grade 3CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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What is a Tangram: A tangram is a traditional Chinese puzzle made of a single square that is cut into 77 specific geometric pieces called 'tans'. These pieces can be arranged to create various shapes like animals, people, or objects.

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The 7 Pieces of a Tangram: A standard tangram set contains exactly 77 pieces: two large triangles, one medium-sized triangle, two small triangles, one square, and one parallelogram. Visually, the two large triangles are identical in size, as are the two small triangles.

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Rules for Creating Shapes: When making a design using tangrams, you must use all 77 pieces. Every piece must touch at least one other piece, but they are not allowed to overlap or lay on top of each other.

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Identifying Geometric Properties: Each tangram piece is a flat shape (2D). You can identify them by their corners (vertices) and sides (edges). For example, the square has 44 corners and 44 equal sides, while each triangle has 33 corners and 33 sides.

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Relationship Between Pieces: The pieces are mathematically related. For instance, if you take the 22 small triangles and place them side-by-side with their longest edges touching, they can perfectly form the small square or the medium triangle.

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The Parallelogram: This is a unique 44-sided shape in the set. It looks like a rectangle that has been tilted or pushed to one side. It has 22 pairs of parallel sides and 44 corners, but unlike the square, its corners are not 'square' (9090 degree) corners.

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Vertices and Edges: In a tangram puzzle, a vertex is the point where two sides meet to form a corner. In a 77-piece set, different shapes have different numbers of vertices. Counting these helps in identifying which piece fits where in a design.

📐Formulae

Total number of pieces in a Tangram set=7\text{Total number of pieces in a Tangram set} = 7

Composition: 5 Triangles+1 Square+1 Parallelogram=7 pieces\text{Composition: } 5 \text{ Triangles} + 1 \text{ Square} + 1 \text{ Parallelogram} = 7 \text{ pieces}

Area relationship: 2×Small Triangle Area=1×Square Area\text{Area relationship: } 2 \times \text{Small Triangle Area} = 1 \times \text{Square Area}

Area relationship: 2×Small Triangle Area=1×Medium Triangle Area\text{Area relationship: } 2 \times \text{Small Triangle Area} = 1 \times \text{Medium Triangle Area}

💡Examples

Problem 1:

Rohan has a 77-piece tangram set. He wants to know the total number of corners (vertices) he would count if he looked at only the square and the two small triangles separately. How many corners are there in total for these three pieces?

Solution:

Step 1: Identify the number of corners on a square. A square has 44 corners. Step 2: Identify the number of corners on one small triangle. A triangle has 33 corners. Step 3: Calculate for two small triangles: 3+3=63 + 3 = 6 corners. Step 4: Add the square's corners to the triangles' corners: 4+6=104 + 6 = 10.

Explanation:

To find the total corners, we sum the vertices of each individual shape. A square contributes 44 vertices and each of the two triangles contributes 33 vertices, leading to 4+(2×3)=104 + (2 \times 3) = 10.

Problem 2:

If a student uses all the pieces of a tangram set to create the shape of a 'Running Man', how many triangles, squares, and parallelograms are used in the design?

Solution:

Step 1: Recall the standard composition of a 77-piece tangram set. Step 2: Count the triangles: There are 22 large, 11 medium, and 22 small triangles, making a total of 55 triangles. Step 3: Count the squares: There is exactly 11 square. Step 4: Count the parallelograms: There is exactly 11 parallelogram.

Explanation:

According to the rules of tangrams, all 77 pieces must be used to create a design. Therefore, any complete tangram figure will always consist of 55 triangles, 11 square, and 11 parallelogram.