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Shapes and Area Properties

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Shapes and Area Properties

Shapes and Area Properties

Geometric shapes illustration

📐 Part 1: Shape Identification

1. Circle the correct name for each shape described:

Shape A: Has exactly one pair of parallel sides

Triangle

Trapezium

Parallelogram

Kite

Shape B: Has two pairs of adjacent equal sides

Triangle

Trapezium

Parallelogram

Kite

Shape C: Has two pairs of parallel sides

Triangle

Trapezium

Parallelogram

Kite

🔍 Part 2: Shape Properties

2. Match each shape to its correct properties:
1. Triangle
2. Kite
3. Trapezium
4. Parallelogram
A. One pair of parallel sides
B. Three sides, angles sum to 180°
C. Two pairs of parallel sides
D. Two pairs of adjacent equal sides
3. Fill in the blanks about shape properties:

A parallelogram has _______ pairs of parallel sides and opposite angles are _______.

A kite has _______ line(s) of symmetry and _______ pairs of adjacent equal sides.

The angles in any triangle always add up to _______ degrees.

📏 Part 3: Area Calculations

4. Calculate the area of each shape using the correct formula. Show your working:

Triangle: Base = 8 cm, Height = 6 cm

Formula: Area = ½ × base × height

Parallelogram: Base = 12 cm, Height = 5 cm

Formula: Area = base × height

Trapezium: Parallel sides = 10 cm and 6 cm, Height = 4 cm

Formula: Area = ½ × (sum of parallel sides) × height

Kite: Diagonal 1 = 8 cm, Diagonal 2 = 6 cm

Formula: Area = ½ × diagonal₁ × diagonal₂

🪞 Part 4: Lines of Symmetry

5. How many lines of symmetry does each shape typically have? Choose the correct answer:

Equilateral Triangle:

0 lines

1 line

3 lines

4 lines

Kite:

0 lines

1 line

2 lines

4 lines

6. Draw the shapes below and mark their lines of symmetry with dashed lines:

Draw an isosceles triangle:

Draw a kite:

🧮 Part 5: Problem Solving

7. A farmer has a triangular paddock with a base of 150 metres and a height of 80 metres. What is the area of the paddock in square metres?
8. A kite-shaped garden has diagonals measuring 12 metres and 8 metres. Calculate the area of the garden.
9. Which properties make a shape a parallelogram? Check all that apply:

Opposite sides are parallel

All angles are 90°

Opposite sides are equal in length

Has exactly 4 lines of symmetry

Opposite angles are equal

💭 Part 6: Reflection

10. Explain in your own words the difference between a parallelogram and a trapezium:
11. Why is it important to know the properties of shapes when calculating their areas?

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