Finding the Perimeter of a Shape with Semicircles | Geometry

Calculating Perimeter of Combined Semicircles

• 🎯 The problem involves finding the perimeter of a shape formed by two smaller semicircles of radius 5 cm and two larger semicircles of radius 10 cm.
• 💡 The key insight is that the two smaller semicircles combine to form a whole circle with a radius of 5 cm, and the two larger semicircles combine to form a whole circle with a radius of 10 cm.

Circumference Calculations

• 📏 The formula for the circumference of a circle is $2 \pi r$.
• 🚀 For the larger combined circle (radius 10 cm), the circumference is $2 \times \pi \times 10 = 20\pi$ cm.
• 🧩 For the smaller combined circle (radius 5 cm), the circumference is $2 \times \pi \times 5 = 10\pi$ cm.

Total Perimeter

• ➕ To find the total perimeter of the entire shape, add the circumferences of the two combined circles: $20\pi$ cm + $10\pi$ cm.
• ✅ The exact perimeter of the shape is 30π centimeters.