Visual Examples: Decomposing Composite Shapes for Area

📚 Quick Study Guide

• 📐 Composite Shapes: These are shapes made up of two or more basic shapes like rectangles, triangles, and circles.
• ➗ Decomposition: The process of breaking down a composite shape into simpler shapes.
• ➕ Area Calculation: Find the area of each simple shape separately, then add them together to find the total area of the composite shape.
• 📏 Rectangle Area: Area of a rectangle = length × width ($A = l \times w$).
• 🔺 Triangle Area: Area of a triangle = $\frac{1}{2}$ × base × height ($A = \frac{1}{2} \times b \times h$).
• 🔵 Circle Area: Area of a circle = π × radius² ($A = \pi \times r^2$). Remember to use approximately 3.14 for π.

Practice Quiz

1. What is the first step in finding the area of a composite shape?
   1. Adding all the side lengths.
   2. Decomposing the shape into simpler shapes.
   3. Measuring the perimeter.
   4. Calculating the volume.
2. A composite shape is made of a rectangle (length = 5cm, width = 3cm) and a triangle (base = 4cm, height = 2cm). What is the total area?
   1. 23 $cm^2$
   2. 19 $cm^2$
   3. 17 $cm^2$
   4. 15 $cm^2$
3. A shape consists of a square (side = 4m) and a semicircle (diameter = 4m). What is the approximate total area? (Use π ≈ 3.14)
   1. 24.28 $m^2$
   2. 20.56 $m^2$
   3. 28.56 $m^2$
   4. 16 $m^2$
4. If a composite shape consists of two identical right triangles, each with a base of 6 inches and a height of 8 inches, what is the total area?
   1. 48 $in^2$
   2. 96 $in^2$
   3. 24 $in^2$
   4. 72 $in^2$
5. A figure is formed by a rectangle (8cm x 5cm) with a smaller rectangle cut out of it (2cm x 3cm). What is the area of the resulting shape?
   1. 34 $cm^2$
   2. 46 $cm^2$
   3. 30 $cm^2$
   4. 40 $cm^2$
6. What is the area of a composite shape made of two squares, one with side 3 and one with side 5?
   1. 8
   2. 16
   3. 34
   4. 25
7. A composite shape is formed by a rectangle (6 x 4) and a triangle with the same base as rectangle width, and height half the rectangle length. Area?
   1. 30
   2. 24
   3. 36
   4. 48