Solved Exercises on Squares in Grade 3

Master squares: identifying properties, calculating perimeter and area, recognizing real-world examples through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Square identification
Exercise 1
Look at this shape. Does it have 4 equal sides? Are all angles right angles? What type of quadrilateral is it?
Definition:

Square: A quadrilateral with 4 equal sides and 4 right angles. It is both a rectangle and a rhombus.

Square identification method:
  1. Count the number of sides (must be 4)
  2. Measure all sides to check if they're equal
  3. Check if all angles are right angles (90°)
  4. Verify opposite sides are parallel
  5. Confirm it's a square based on properties
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Sides: 4 (all equal)
Angles: 4 (all 90°)
Parallel sides: 2 pairs
Name: Square
Step 1: Count the sides

This shape has 4 sides

Step 2: Check side lengths

All 4 sides are equal in length

Step 3: Check angles

All 4 angles are right angles (90°)

Step 4: Check parallel sides

Opposite sides are parallel

Step 5: Identify the shape

It's a square (has all properties)

Square: 4 equal sides, 4 right angles
Final answer:

This is a square with 4 equal sides and 4 right angles.

Applied rules:

• Square definition: 4 equal sides + 4 right angles

• Quadrilateral: 4-sided polygon

• Right angle: 90° angle

2 Perimeter calculation
Exercise 2
A square has sides that are each 5 cm long. What is the perimeter of the square?
Definition:

Perimeter: The total distance around the outside of a shape. For a square: P = 4 × side length.

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Side length: 5 cm
Formula: P = 4s
Calculation: 4 × 5 = 20 cm
Step 1: Identify the side length

Each side of the square is 5 cm

Step 2: Apply the perimeter formula

Perimeter = 4 × side length

Step 3: Substitute the value

Perimeter = 4 × 5 cm

Step 4: Calculate

Perimeter = 20 cm

Step 5: State the answer

The perimeter is 20 cm

Perimeter = 20 cm
Final answer:

The perimeter of the square is 20 cm.

Applied rules:

• Square perimeter: P = 4s (where s is side length)

• Multiplication: 4 equal sides added together

• Units: Keep the same unit (cm)

3 Area calculation
Exercise 3
A square has sides that are each 6 inches long. What is the area of the square?
Definition:

Area: The amount of space inside a shape. For a square: A = side length × side length = s².

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Side length: 6 in
Formula: A = s²
Calculation: 6 × 6 = 36 sq in
Step 1: Identify the side length

Each side of the square is 6 inches

Step 2: Apply the area formula

Area = side length × side length

Step 3: Substitute the value

Area = 6 × 6 inches

Step 4: Calculate

Area = 36 square inches

Step 5: State the answer

The area is 36 square inches

Area = 36 square inches
Final answer:

The area of the square is 36 square inches.

Applied rules:

• Square area: A = s² (where s is side length)

• Multiplication: Side × side

• Units: Square units (sq in)

Rules and methods, laws,...
Square: 4 equal sides, 4 right angles
Square Definition
Perimeter
P = 4s
4 times side length
Area
A = s²
Side length squared
Properties
Equal sides, right angles
Special rectangle/rhombus
Key definitions:

Square: A quadrilateral with 4 equal sides and 4 right angles.

Quadrilateral: A polygon with 4 sides and 4 vertices.

Right angle: An angle that measures exactly 90°.

Perimeter: The total distance around the outside of a shape.

Area: The amount of space inside a shape.

Complete methodology:
  1. Identify the shape: Confirm it's a square by checking properties
  2. Measure sides: Verify all 4 sides are equal
  3. Check angles: Confirm all 4 angles are 90°
  4. Apply formulas: Use correct formulas for perimeter and area
  5. Calculate: Perform accurate calculations
Tip 1: All squares are rectangles, but not all rectangles are squares.
Tip 2: To check for right angles, use the corner of a piece of paper.
Tip 3: Perimeter is measured in linear units (cm, in, ft).
Tip 4: Area is measured in square units (sq cm, sq in, sq ft).
Common errors: Confusing perimeter with area, using wrong formulas, forgetting to square units for area.
Memory aid: "Square" sounds like "equal" - all sides are equal.
Key formulas:

• Perimeter of square: P = 4s

• Area of square: A = s²

• Diagonal of square: d = s√2

• All sides equal: s₁ = s₂ = s₃ = s₄

Solution: Exercises 4 to 5
4 Properties analysis
Exercise 4
A square has sides of 8 cm. What are all its properties? Calculate perimeter and area.
Definition:

Square properties: 4 equal sides, 4 right angles, 2 pairs of parallel sides, 2 equal diagonals that bisect each other.

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Side length: 8 cm
Perimeter: 4 × 8 = 32 cm
Area: 8² = 64 sq cm
Angles: 4 right angles
Step 1: Identify all properties

4 equal sides of 8 cm, 4 right angles, parallel opposite sides

Step 2: Calculate perimeter

P = 4 × 8 = 32 cm

Step 3: Calculate area

A = 8 × 8 = 64 square cm

Step 4: Note special properties

Diagonals are equal and bisect each other at right angles

Step 5: State all answers

Perimeter = 32 cm, Area = 64 sq cm

Perimeter = 32 cm, Area = 64 sq cm
Final answer:

The square has 4 equal sides of 8 cm, 4 right angles, perimeter of 32 cm, and area of 64 square cm.

Applied rules:

• Square properties: All sides equal, all angles 90°

• Perimeter formula: P = 4s

• Area formula: A = s²

5 Real-world application
Exercise 5
A square tile has sides of 10 inches. How much area does it cover? How much border would be needed?
Definition:

Real-world application: Using square properties to solve practical problems involving area and perimeter.

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Side length: 10 in
Area (coverage): 10² = 100 sq in
Perimeter (border): 4 × 10 = 40 in
Step 1: Identify the problem

Need to find area (coverage) and perimeter (border)

Step 2: Calculate area for coverage

Area = 10 × 10 = 100 square inches

Step 3: Calculate perimeter for border

Perimeter = 4 × 10 = 40 inches

Step 4: Interpret results

The tile covers 100 sq in and needs 40 in border

Step 5: State the answer

Area = 100 sq in, Perimeter = 40 in

Area = 100 sq in, Perimeter = 40 in
Final answer:

The square tile covers 100 square inches of area and needs 40 inches of border.

Applied rules:

• Area for coverage: A = s²

• Perimeter for border: P = 4s

• Real-world context: Units match practical applications

Detailed Summary: Squares
Square: 4 equal sides, 4 right angles
Core Square Definition
Key definitions:

Square: A quadrilateral with 4 equal sides and 4 right angles. It is the most symmetrical quadrilateral.

Quadrilateral: A polygon with exactly 4 sides and 4 vertices.

Right angle: An angle that measures exactly 90°.

Perimeter: The total distance around the outside of a shape (linear measurement).

Area: The amount of space inside a shape (square measurement).

Parallel lines: Lines that never intersect and stay the same distance apart.

Diagonal: A line connecting opposite vertices of a square.

Complete methodology for working with squares:
  1. Identification: Verify the shape has 4 equal sides and 4 right angles
  2. Measurement: Determine the side length
  3. Formula selection: Choose the correct formula (perimeter vs area)
  4. Calculation: Apply the formula accurately
  5. Unit verification: Ensure correct units (linear for perimeter, square for area)
  6. Application: Interpret results in real-world context
Tip 1: Remember that all squares are both rectangles AND rhombuses, but not all rectangles or rhombuses are squares.
Tip 2: To check for right angles, use a corner of paper - if it fits perfectly, it's a right angle.
Tip 3: For perimeter, multiply the side length by 4 (P = 4s).
Tip 4: For area, multiply the side length by itself (A = s²).
Tip 5: The diagonals of a square are equal in length and bisect each other at right angles.
Common errors: Mixing up perimeter and area formulas, forgetting to square units for area, confusing squares with other quadrilaterals.
Memory aids: "Square" sounds like "equal" - all sides are equal. "Area" starts with "A" like "All" the space inside.
Real-world applications: Floor tiles, picture frames, chess boards, stamps, windows, doors, fabric squares, game pieces.
Essential rules to remember:

• Rule 1: All 4 sides of a square are equal in length

• Rule 2: All 4 angles of a square are right angles (90°)

• Rule 3: Opposite sides are parallel

• Rule 4: Perimeter formula: P = 4s

• Rule 5: Area formula: A = s²

• Rule 6: Diagonals are equal and bisect at 90°

P = 4s, A = s², d = s√2
Key Formulas
Problem-solving strategies:

• Strategy 1: Always verify that all sides are equal before calling a shape a square

• Strategy 2: Draw a diagram to visualize the problem

• Strategy 3: Label all known measurements on the diagram

• Strategy 4: Choose the correct formula based on what you need to find

• Strategy 5: Check your answer by ensuring units are correct

Questions & Answers

Question: I'm not sure how to tell if a shape is really a square. How can I check?

Answer: Great question! To check if a shape is a square, you need to verify two main things:

  • 4 equal sides: All four sides must be the same length
  • 4 right angles: All four angles must be exactly 90° (right angles)

You can use a ruler to measure the sides and a corner of paper to check the angles. If both conditions are met, then it's definitely a square!

Remember: All squares are rectangles, but not all rectangles are squares.

Question: My child gets confused between perimeter and area. Any tips for helping them understand the difference?

Answer: Here are some helpful ways to distinguish between perimeter and area:

  • Perimeter: Think "fence around" or "walk around the edge" - it's the distance around the outside
  • Area: Think "fill inside" or "cover the surface" - it's the space inside the shape

You can demonstrate with a square:

  • Perimeter = the length of string needed to go around the square
  • Area = the number of small squares that fit inside the big square

Also remember: perimeter uses linear units (cm, in) while area uses square units (sq cm, sq in).

Question: Why do we need to learn about squares? When will I ever use this in real life?

Answer: Squares are everywhere in real life! Here are practical examples:

  • Construction: Floor tiles, window panes, and room layouts are often square
  • Crafting: Making picture frames, quilting, or building with blocks
  • Shopping: Understanding carpet sizes, wallpaper coverage, or garden plot areas
  • Games: Chess boards, checker boards, and many board games use squares
  • Technology: Computer screens and many electronic devices have square or rectangular shapes

Knowing about squares helps you understand measurements, patterns, and shapes in the world around you!