หน่วย 1 แผน 1 tangram worksheet | PDF - Free Printable

It looks like you've uploaded a worksheet from Sialkot Grammar School related to a Tangram puzzle, which is a traditional Chinese dissection puzzle consisting of seven flat shapes (tans) that can be arranged to form various shapes. The task involves analyzing the geometric properties and relative areas of the pieces.

Let’s solve each question step by step based on standard Tangram knowledge and the image provided (which I can't see, but I’ll assume it's a standard tangram layout with labeled pieces 1 through 7).

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🔷 Standard Tangram Pieces:

A classic tangram set has 7 pieces:
- 5 triangles: 2 large, 1 medium, 2 small
- 1 square
- 1 parallelogram

The total area of all pieces together forms a large square.

We are told:
> "Let area of piece 3 equal to 1"

From standard tangram geometry:
- All pieces are derived from a square.
- The small triangle (piece 3) has area = 1 unit.
- Then we can deduce the areas of other pieces in terms of this.

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✔ Let's Solve Each Question:

#### 1. How many pieces of tangram?
✔ Answer: 7

There are always 7 pieces in a tangram set.

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#### 2. Which pieces are right angle triangles?
Right-angle triangles are those with one 90° angle.

All triangles in tangram are right-angled.

So:
- Piece 1 – large right triangle
- Piece 2 – large right triangle
- Piece 3 – small right triangle
- Piece 4 – small right triangle
- Piece 5 – medium right triangle

✔ Answer: Pieces 1, 2, 3, 4, 5

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#### 3. Which pieces are squares?
Only one square exists in a tangram.

That’s Piece 6

✔ Answer: Piece 6

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#### 4. Which pieces are parallelogram?
Only one parallelogram in tangram.

That’s Piece 7

✔ Answer: Piece 7

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#### 5. Which pieces have equal area?
Now let’s analyze areas using the assumption:
> Area of piece 3 = 1

From standard tangram proportions:
- Small triangle (piece 3): area = 1
- Other small triangle (piece 4): same as piece 3 → area = 1
- Medium triangle (piece 5): area = 2
- Square (piece 6): area = 2
- Parallelogram (piece 7): area = 2
- Large triangle (piece 1): area = 4
- Large triangle (piece 2): area = 4

So:
- Piece 3 and Piece 4 → both area = 1 → equal
- Piece 5, 6, 7 → all area = 2 → equal
- Piece 1 and Piece 2 → both area = 4 → equal

✔ Answer:
- Piece 3 and Piece 4 have equal area
- Piece 5, 6, and 7 have equal area
- Piece 1 and Piece 2 have equal area

(You may list them as: 3 & 4; 5, 6, 7; 1 & 2)

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#### 6. How many area of piece 1 per area of total?
Area of piece 1 = 4
Total area = sum of all pieces = 1+1+2+2+2+4+4 = 16

So:
4 / 16 = 1/4

✔ Answer: 1/4

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#### 7. How many area of piece 2 per area of piece 1?
Both piece 1 and 2 have area = 4
So: 4 / 4 = 1

✔ Answer: 1

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#### 8. How many area of piece 7 per area of total?
Area of piece 7 = 2
Total = 16
So: 2 / 16 = 1/8

✔ Answer: 1/8

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#### 9. How many area of piece 3 per area of piece 4?
Both piece 3 and 4 have area = 1
So: 1 / 1 = 1

✔ Answer: 1

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#### 10. How many area of piece 3 per area of piece 5?
Piece 3 = 1, Piece 5 = 2
So: 1 / 2 = 0.5

✔ Answer: 0.5 or 1/2

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#### 11. How many area of piece 4 per area of piece 6?
Piece 4 = 1, Piece 6 = 2
So: 1 / 2 = 0.5 or 1/2

✔ Answer: 0.5 or 1/2

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#### 12. If area of piece 1 equal to 4, what is area of total?
We're told: area of piece 1 = 4
But earlier we said piece 1 = 4 units when piece 3 = 1 → so scale matches.

So total area = 16 (as calculated above)

✔ Answer: 16

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✔ Final Answer for the Last Part:

> Let area of piece 3 equal to 1, so you will get area of each piece equal to
> Piece 1 : Piece 2 : Piece 3 : Piece 4 : Piece 5 : Piece 6 : Piece 7
> ______ : ______ : 1 : ______ : ______ : ______ : ______

Now fill in:
- Piece 1 = 4
- Piece 2 = 4
- Piece 3 = 1
- Piece 4 = 1
- Piece 5 = 2
- Piece 6 = 2
- Piece 7 = 2

✔ So the line becomes:
> 4 : 4 : 1 : 1 : 2 : 2 : 2

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✔ Summary of Answers:

| Question | Answer |
|--------|--------|
| 1 | 7 |
| 2 | Pieces 1, 2, 3, 4, 5 |
| 3 | Piece 6 |
| 4 | Piece 7 |
| 5 | Piece 3 & 4; Piece 5, 6, 7; Piece 1 & 2 |
| 6 | 1/4 |
| 7 | 1 |
| 8 | 1/8 |
| 9 | 1 |
| 10 | 1/2 |
| 11 | 1/2 |
| 12 | 16 |
| Final row | 4 : 4 : 1 : 1 : 2 : 2 : 2 |

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Let me know if you'd like a visual explanation or help drawing the tangram!