Real-world examples: calculating missing dimensions of shapes

📚 Quick Study Guide

• 📐 Area of a Rectangle: Area = Length × Width. If you know the area and one side, you can find the other by dividing the area by the known side. $Width = \frac{Area}{Length}$
• 📏 Perimeter of a Rectangle: Perimeter = 2 × (Length + Width). If you know the perimeter and one side, you can find the other using algebra. $Width = (\frac{Perimeter}{2}) - Length$
• ⛰️ Area of a Triangle: Area = $\frac{1}{2}$ × Base × Height. If you know the area and the base (or height), you can find the missing height (or base). $Height = \frac{2 × Area}{Base}$
• 🔵 Area of a Circle: Area = $πr^2$ where r is the radius. If you know the area, you can calculate the radius by $r = \sqrt{\frac{Area}{π}}$
• 🔄 Circumference of a Circle: Circumference = $2πr$ where r is the radius. If you know the circumference, the radius can be found by $r = \frac{Circumference}{2π}$

✏️ Practice Quiz

1. What is the width of a rectangle with an area of 48 square meters and a length of 8 meters?
   1. 6 meters
   2. 7 meters
   3. 8 meters
   4. 9 meters
2. A rectangle has a perimeter of 30 cm and a length of 9 cm. What is its width?
   1. 5 cm
   2. 6 cm
   3. 7 cm
   4. 8 cm
3. A triangle has an area of 24 square inches and a base of 8 inches. What is its height?
   1. 4 inches
   2. 5 inches
   3. 6 inches
   4. 7 inches
4. The area of a circle is approximately 78.5 square feet. What is the radius, using $π ≈ 3.14$?
   1. 3 feet
   2. 4 feet
   3. 5 feet
   4. 6 feet
5. A circular garden has a circumference of 62.8 meters. What is its radius, using $π ≈ 3.14$?
   1. 8 meters
   2. 9 meters
   3. 10 meters
   4. 11 meters
6. A rectangular banner has an area of 36 square feet. If the width is 4 feet, what is the length?
   1. 7 feet
   2. 8 feet
   3. 9 feet
   4. 10 feet
7. A triangle has a height of 10 cm and an area of 35 square cm. What is the length of the base?
   1. 5 cm
   2. 6 cm
   3. 7 cm
   4. 8 cm