Real-world examples of area of composite figures with circles (Grade 7).

📚 Quick Study Guide

• 📐 Area of a Circle: The area of a circle is found using the formula $A = \pi r^2$, where $r$ is the radius and $\pi$ (pi) is approximately 3.14.
• ➕ Area of a Rectangle: The area of a rectangle is found using the formula $A = l \times w$, where $l$ is the length and $w$ is the width.
• ➖ Area of a Square: The area of a square is found using the formula $A = s^2$, where $s$ is the length of a side.
• 🧩 Composite Figures: These are shapes made up of two or more basic shapes. To find the area, calculate the area of each individual shape and then add or subtract them as needed.
• 💡 Key Strategy: Identify the basic shapes within the composite figure. Decide whether to add (if the shapes are combined) or subtract (if one shape is cut out of another) the areas.

Practice Quiz

1. What is the area of a composite figure made of a rectangle (length 10 cm, width 5 cm) with a semicircle (radius 2.5 cm) on one of its widths?
   1. 34.81 cm²
   2. 59.81 cm²
   3. 64.90 cm²
   4. 44.63 cm²
2. A square (side 8 cm) has a circle (radius 3 cm) cut out from its center. What is the area of the remaining composite figure?
   1. 64 cm²
   2. 28.26 cm²
   3. 35.74 cm²
   4. 55.74 cm²
3. A figure consists of a rectangle (length 12 cm, width 6 cm) and two identical circles (radius 2 cm) attached to the shorter sides. What is the total area of the figure?
   1. 72 cm²
   2. 25.12 cm²
   3. 97.12 cm²
   4. 122.24 cm²
4. A composite figure is made up of a square (side 6 cm) with a quarter circle (radius 6 cm) removed from one corner. Find the area of the composite figure.
   1. 36 cm²
   2. 28.26 cm²
   3. 7.74 cm²
   4. 44.26 cm²
5. What is the area of a composite figure formed by a circle (radius 5 cm) and an equilateral triangle (side 5 cm) inside the circle?
   1. 78.5 cm²
   2. 10.83 cm²
   3. 89.33 cm²
   4. 67.67 cm²
6. A running track is shaped like a rectangle with two semicircles at each end. The rectangle is 80 m long, and the diameter of each semicircle is 60 m. What is the area enclosed by the track?
   1. 4800 m²
   2. 2826 m²
   3. 7626 m²
   4. 12452 m²
7. A window consists of a square (side 4 ft) with a semicircle on top of it (diameter 4 ft). What is the total area of the window?
   1. 16 ft²
   2. 6.28 ft²
   3. 22.28 ft²
   4. 10.28 ft²