Composite Shapes Area Perimeter

Composite Shapes Area & Perimeter

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📐 Part 1: Understanding Composite Shapes

1. What is a composite shape? Circle the best definition:

A shape with only straight sides

A shape made by joining two or more simple shapes together

A shape that is always a rectangle

A shape with curved edges only

2. Which of these are simple shapes that can make composite shapes? Check all that apply:

Rectangle

Triangle

Circle

Square

3. Draw a composite shape made from one rectangle and one triangle:

📏 Part 2: Calculating Perimeter

4. A composite shape is made from a rectangle (6cm × 4cm) with a triangle (base 6cm, height 3cm) attached to the top. The triangle's slanted sides are each 3.6cm long. Calculate the perimeter.

Step 1: Draw and label the composite shape:

Step 2: Show your working:

Answer: Perimeter = _________ cm

5. Fill in the blanks about calculating perimeter:

To find the perimeter of a composite shape, I need to add up all the _____________ side lengths. I must be careful not to include any _____________ lines where shapes are joined together.

📐 Part 3: Calculating Area

6. Using the same composite shape from Question 4 (rectangle 6cm × 4cm with triangle base 6cm, height 3cm on top), calculate the total area.

Step 1: Calculate the area of the rectangle:

Area of rectangle = length × width = _____ × _____ = _____ cm²

Step 2: Calculate the area of the triangle:

Area of triangle = ½ × base × height = ½ × _____ × _____ = _____ cm²

Step 3: Calculate the total area:

Total area = _____ + _____ = _____ cm²

7. Match the formula to the correct shape:

1. Rectangle

2. Triangle

3. Square

A. ½ × base × height

B. side × side

C. length × width

🧮 Part 4: Problem Solving

8. A house-shaped composite figure is made from a square base (8m × 8m) with a triangular roof (base 8m, height 5m). Calculate both the perimeter and area. The slanted roof sides are each 6.4m long.

Sketch the shape with labels:

Calculate the perimeter:

Calculate the area:

Final Answers:

Perimeter = _________ metres

Area = _________ square metres

9. A composite shape is made by removing a small rectangle (2cm × 3cm) from the corner of a larger rectangle (10cm × 8cm). What is the area of the remaining shape?

Answer: _________ cm²