Solved Exercises on Composing Shapes in Grade 1

Master composing shapes: combining triangles, squares, rectangles, and circles to create new figures through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Combining Two Triangles
Exercise 1
If you put together 2 triangles, what new shape can you make?
🔺 + 🔺 → ❓
Definition:

Composing shapes: Putting smaller shapes together to make bigger shapes.

Method:
  1. Look at the shapes you have
  2. Think about how they fit together
  3. Try different arrangements
  4. See what new shape is formed
Starting shapes
2 triangles
New shape
Square or Rhombus
Step 1: Identify the starting shapes

We have 2 triangles: 🔺 🔺

Step 2: Arrange the triangles

Place them together side by side or corner to corner

Step 3: Observe the new shape

When placed correctly, 2 triangles can form a square or rhombus

2 triangles → Square or Rhombus
Final answer:

When you put together 2 triangles, you can make a square or rhombus!

Applied rules:

• Shape combination: Smaller shapes can form larger shapes

• Rotation: Shapes can be turned to fit together

• Pattern recognition: Look for familiar arrangements

🔺 🔺 → ⬜
2 Rectangle from Squares
Exercise 2
How many squares do you need to make a rectangle?
⬜ + ⬜ → ▭
Definition:

Rectangle: A shape with 4 sides where opposite sides are equal.

Starting shapes
Squares
Target shape
Rectangle
Number needed
2 or more
Step 1: Start with squares

Each square has 4 equal sides: ⬜

Step 2: Arrange squares side by side

Put 2 squares next to each other: ⬜⬜

Step 3: Count the result

You now have a longer shape with 4 sides: a rectangle!

2 squares → Rectangle
Final answer:

You need 2 squares to make a rectangle!

Applied rules:

• Side matching: Equal sides fit perfectly together

• Length addition: Adding lengths creates longer shapes

• Shape preservation: Rectangles have 4 right angles

⬜ ⬜ → ▭▭
3 Hexagon from Triangles
Exercise 3
How many triangles do you need to make a hexagon?
🔺 + 🔺 + 🔺 + 🔺 + 🔺 + 🔺 → ⬡
Definition:

Hexagon: A shape with 6 sides and 6 corners.

Starting shapes
Triangles
Target shape
Hexagon
Number needed
6 triangles
Step 1: Understand the target

A hexagon has 6 sides and 6 corners

Step 2: Think about triangles

Each triangle can represent one side of the hexagon

Step 3: Arrange triangles

Put 6 triangles together in a circle pattern

Step 4: Count the result

6 triangles arranged properly form a hexagon

6 triangles → Hexagon
Final answer:

You need 6 triangles to make a hexagon!

Applied rules:

• Side count: Number of sides equals number of triangles

• Circular arrangement: Triangles meet at a center point

• Angle consideration: 360° divided by 6 = 60° per triangle

🔺 🔺 🔺 🔺 🔺 🔺 → ⬡
Rules and methods, laws,...
🔺 + 🔺 = ⬛ or ⬢
Triangle Combination
Rule 1
2 squares = rectangle
Combining equal shapes
Rule 2
6 triangles = hexagon
Radial symmetry
Rule 3
2 rectangles = larger rectangle
Linear arrangement
Key definitions:

Triangle: 3-sided shape with 3 corners

Square: 4 equal sides and 4 right angles

Rectangle: 4 sides with opposite sides equal

Circle: Round shape with no corners

Hexagon: 6-sided shape

Complete methodology:
  1. Identify shapes: Name the shapes you have
  2. Plan arrangement: Think about how they fit together
  3. Count sides: Match equal sides when possible
  4. Visualize result: Predict the new shape
  5. Verify: Check if the new shape makes sense
Tip 1: Try rotating shapes to find the best fit.
Tip 2: Equal sides match perfectly when joined.
Tip 3: Count corners and sides to identify new shapes.
Tip 4: Circles are special - they don't combine like polygons.
Common combinations: 2 triangles = square/rhombus, 2 squares = rectangle, 4 triangles = square.
Key insight: The number of sides often determines how shapes combine.
Formulas to know by heart:

• 2 triangles → square or rhombus

• 2 squares → rectangle

• 4 triangles → square

• 6 triangles → hexagon

• 2 rectangles → larger rectangle

Exercise with Visualization: Shape Combinations
Exercise 6: Shape Combinations Table
Consider the following shape combinations:
🔺 + 🔺 → ⬛ (Triangle + Triangle = Square)
⬜ + ⬜ → 📐 (Square + Square = Rectangle)
🔺 + 🔺 + 🔺 + 🔺 → ⬛ (4 Triangles = Square)
Starting Shapes Combination Result
2 Triangles 🔺 + 🔺 Square/Rhombus
2 Squares ⬜ + ⬜ Rectangle
4 Triangles 🔺 + 🔺 + 🔺 + 🔺 Square
6 Triangles 6 × 🔺 Hexagon

Analysis: The table shows how different combinations of basic shapes create new geometric figures.

  • Triangular arrangements often form quadrilaterals
  • Linear arrangements create longer versions of shapes
  • Circular arrangements form polygons with multiple sides

Questions & Answers

Question: I have 3 triangles, but when I put them together I don't get a square. Why?

Answer: Great observation! That's because triangles have 3 sides, but squares have 4 sides. You need 2 specific triangles to form a square or rhombus, not 3.

  • With 2 triangles: 🔺 + 🔺 → ⬛ (Square or Rhombus)
  • With 3 triangles: 🔺 + 🔺 + 🔺 → ❌ (Not a square)
  • With 4 triangles: 🔺 + 🔺 + 🔺 + 🔺 → ⬛ (Square)

Three triangles together might form a different shape, like a larger triangle or an irregular shape. Remember, the number of sides matters when combining shapes!

Example: 2 right triangles with equal legs can form a square when placed hypotenuse-to-hypotenuse.

Question: My child is struggling to see how shapes combine. Are there any hands-on activities to help visualize this better?

Answer: Absolutely! Hands-on activities work wonderfully for young learners:

  • Paper cutting: Cut out triangles, squares, and rectangles from colored paper to physically combine them
  • Pattern blocks: Use wooden or foam geometric shapes that fit together
  • Toothpicks and marshmallows: Build shapes by connecting with toothpicks
  • Shape puzzles: Tangram sets allow children to create new shapes from smaller pieces

These tactile experiences help children understand spatial relationships and develop their visual-spatial skills, which are crucial for geometry.

Start with simple combinations like 2 triangles making a square, then progress to more complex arrangements.

Question: Can I make a circle using triangles?

Answer: That's a creative thought! While you can't make a perfect circle using triangles, you can make a shape that looks very close to a circle.

  • With just a few triangles, you'll get a pointy shape
  • If you use many, many small triangles arranged in a circle pattern, it starts to look round
  • This is actually how computers draw circles - with many tiny straight lines!

But in basic geometry for grade 1, we focus on combining shapes that fit together perfectly with straight edges, like squares, triangles, and rectangles.

For now, remember that circles are special shapes that don't combine like polygons with straight sides.