Composite Figure Area

Grade 6 · geometry · 100 practice problems · read aloud

🔊 Listen to this explanation

Finding the Area of Composite Figures

🧩 What is a Composite Figure?

A composite figure is a shape made by putting together two or more simple shapes, like rectangles, triangles, or squares. We find their total area by breaking them apart. This is super useful for real-life problems, like figuring out how much paint you need for a wall with a window in it, or how much carpet for an L-shaped room!

📝 Step-by-Step Guide

  1. Step 1: Divide - Look at the figure and decide how to split it into simpler shapes that you know how to work with.
  2. Step 2: Find Missing Lengths - Use the given side lengths to find any missing measurements you'll need for your formulas.
  3. Step 3: Calculate Each Area - Use the correct area formula for each simple shape.
  4. Step 4: Add (or Subtract) - Add all the areas together. If there's a piece cut out (like a hole), subtract its area.

🔍 Worked Examples

Example 1: An "L"-Shape

Imagine an "L" made of two rectangles. Rectangle A is 10 ft by 4 ft. Rectangle B is 6 ft by 4 ft.

  1. Divide: We already have two rectangles.
  2. Calculate Areas:
    Area of A = 10 × 4 = 40 sq ft
    Area of B = 6 × 4 = 24 sq ft
  3. Add: Total Area = 40 + 24 = 64 sq ft.

Example 2: A House Shape

A square (8 m by 8 m) with a triangle on top (base 8 m, height 4 m).

  1. Divide: One square and one triangle.
  2. Calculate Areas:
    Area of Square = 8 × 8 = 64 sq m
    Area of Triangle = (½) × 8 × 4 = 16 sq m
  3. Add: Total Area = 64 + 16 = 80 sq m.

⚠️ Common Mistakes to Avoid

  • Forgetting Units: Always label your answer with square units (e.g., sq cm, ft²).
  • Missing Lengths: Carefully find all missing side lengths before calculating. Don't just use the numbers you see!
  • Wrong Triangle Formula: The area of a triangle is ½ × base × height, not base × height.
  • Double-Counting: Make sure the pieces you add don't overlap.

💡 Tips & Tricks

  • Draw It! Redraw the figure and split it with dotted lines. This makes it much easier to see the parts.
  • Check Your Logic: Does your final answer make sense? Is it roughly the size you'd expect?
  • Formula Friend: Keep a list of area formulas (rectangle, square, triangle) handy while you work.

🎯 How to Practice

The best way to get good at this is to practice!

  • Find practice problems in your textbook or online worksheets.
  • Look for composite figures in real life! What is the area of your bedroom floor? A garden in your yard?
  • Challenge a friend to solve the same problem and compare your methods.

Practice problems

6 of the 100, worked through step by step — try them before opening the answer.

1 15% of 2400 = ?

Hint: To find a percentage of a number, you can convert the percentage to a decimal and then multiply by the number.

Show the answer

Answer: 360

  1. Understand that "percent" means "per hundred". So 15% means 15 per 100, which can be written as 15/100.
  2. "Of" in mathematics usually means multiplication. So 15% of 2400 means: (15/100) × 2400
  3. Simplify the calculation. We can write it as: 15 × (2400 / 100)
  4. First compute 2400 divided by 100. 2400 / 100 = 24
  5. Now multiply: 15 × 24 = 360 Therefore, 15% of 2400 = 360.

We want to calculate 15% of 2400.

2 (15² - 12²) ÷ 9 = ?

Hint: Remember to calculate the squares first before performing the subtraction, then divide the result by the given number.

Show the answer

Answer: 9

  1. Calculate the squares. 15 squared is 15 × 15 = 225. 12 squared is 12 × 12 = 144.
  2. Subtract the squares. 225 − 144 = 81.
  3. Divide the result by 9. 81 ÷ 9 = 9. Final answer: 9

Let's solve step-by-step.

3 (15² - 12²) ÷ (3 × 4) = ?

Hint: Remember to calculate the squares first, then perform the subtraction, and finally divide by the product. Consider using the difference of squares pattern as an alternative approach.

Show the answer

Answer: 6.75

  1. Calculate the squares** 15² = 15 × 15 = 225 12² = 12 × 12 = 144 **
  2. Subtract inside the parentheses** 225 - 144 = 81 So the expression becomes: 81 ÷ (3 × 4) **
  3. Multiply in the denominator** 3 × 4 = 12 Now we have: 81 ÷ 12 **
  4. Perform the division** 81 ÷ 12 = 81/12 **
  5. Simplify the fraction** Both 81 and 12 can be divided by 3: 81 ÷ 3 = 27 12 ÷ 3 = 4 So 81/12 = 27/4 **
  6. Convert to decimal** 27/4 = 6.75 **Final Answer:** 6.75

Let's solve step-by-step. We have: (15² - 12²) ÷ (3 × 4) = ? **

4 (15 × 8) + (½ × 15 × 6) = ?

Hint: Break the problem into simpler shapes, calculate each area separately, then combine them.

Show the answer

Answer: 165

  1. Calculate the first part** 15 × 8 = 120 **
  2. Calculate the second part** First, ½ × 15 = 15/2 = 7.5 Then, 7.5 × 6 = 45 Alternatively, you can compute it as: ½ × 15 × 6 = (15 × 6) / 2 = 90 / 2 = 45 **
  3. Add both parts** 120 + 45 = 165 **Final Answer:** 165

Let's solve step by step. We have: (15 × 8) + (½ × 15 × 6) **

5 (3/4 × 48) + (2/3 × 36) = ?

Hint: When working with expressions that have multiple operations, remember to follow the order of operations. First perform the multiplications inside the parentheses, then add the results together.

Show the answer

Answer: 60

  1. Calculate 3/4 × 48 3/4 × 48 means (3 × 48) ÷ 4. First, 3 × 48 = 144. Then 144 ÷ 4 = 36. So 3/4 × 48 = 36.
  2. Calculate 2/3 × 36 2/3 × 36 means (2 × 36) ÷ 3. First, 2 × 36 = 72. Then 72 ÷ 3 = 24. So 2/3 × 36 = 24.
  3. Add the two results 36 + 24 = 60. Final Answer: 60

Let's solve step by step. We have: (3/4 × 48) + (2/3 × 36)

6 (12 × 15) + (3.14 × 6²) = ?

Hint: Remember to calculate the area of each shape separately, then combine them. For a circle, use the formula π × radius².

Show the answer

Answer: 293.04

  1. Calculate the area of the rectangle: 12 × 15 = 180
  2. Calculate the area of the circle: First find radius squared: 6² = 36
  3. Multiply by π: 3.14 × 36 = 113.04
  4. Add the two areas: 180 + 113.04 = 293.04

The answer is 293.04.

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