Semicircles: calculate area, perimeter, radius, and diameter

Learning Objectives Identify and label the radius and diameter of a semicircle. Calculate the radius of a semicircle given its diameter, and vice versa. Apply the formula to calculate the area of a semicircle. Apply the formula to calculate the perimeter of a semicircle. Solve problems involving finding the area, perimeter, radius, or diameter of semicircles using $\pi \approx 3.14$. Distinguish between the area and perimeter of a semicircle. Ever wondered how much space a half-moon rug covers or how much trim you'd need to go around a semicircular window? 🌙 In this lesson, you'll learn all about semicircles – what they are, their key parts, and how to calculate their area, perimeter, radius, and diameter. Understanding these measurements helps us solve real-worl...

TermDefinitionExample SemicircleA semicircle is exactly half of a circle. It has a curved edge and a straight edge (which is the diameter of the original circle).If you cut a round pizza exactly in half, each piece is a semicircle. CircleA circle is a perfectly round shape where all points on its edge are the same distance from its center.A coin, a clock face, or a bicycle wheel are all examples of circles. Radius (r)The radius is the distance from the center of a circle (or semicircle) to any point on its curved edge.If a semicircle has a center point, the distance from that center to the curved part is its radius. Diameter (d)The diameter is the distance across a circle (or the straight edge of a semicircle) passing through its center. It's twice the length of the radius.The straig...

Radius and Diameter Relationship $r = \frac{d}{2}$ or $d = 2r$ To find the radius (r) when you know the diameter (d), divide the diameter by 2. To find the diameter (d) when you know the radius (r), multiply the radius by 2. Area of a Semicircle $A = \frac{1}{2} \pi r^2$ To find the area (A) of a semicircle, calculate the area of a full circle ($\pi r^2$) and then divide it by 2. Remember to use $\pi \approx 3.14$ and 'r' for radius. The unit for area is always squared (e.g., cm$^2$, m$^2$). Perimeter of a Semicircle $P = \pi r + d$ To find the perimeter (P) of a semicircle, you add the length of its curved arc (which is half the circumference of a full circle, $\pi r$) to the length of its straight diameter (d). Alternatively, since $d=2r$, you can use...