Area of Semicircles
Area of semicircles is a Grade 7 geometry concept in Big Ideas Math Advanced 2, Chapter 13: Circles and Area. Since a semicircle is half of a full circle, its area equals pi times r squared divided by 2. For example, a semicircle with radius 4 units has area 8 pi square units, and if the diameter is given, divide by 2 first to get the radius.
Key Concepts
The area of a semicircle is half the area of a full circle: $$A = \frac{\pi r^2}{2}$$.
where $r$ is the radius of the semicircle.
Common Questions
What is the formula for the area of a semicircle?
The area of a semicircle is A equals pi times r squared divided by 2, which is half the area of a complete circle with the same radius.
How do you find the area of a semicircle when given the diameter?
Divide the diameter by 2 to get the radius, then apply A equals pi times r squared divided by 2. For example, a semicircle with diameter 10 has radius 5, so area equals 25 pi divided by 2.
How is semicircle area used in composite figure problems?
Composite figures often include semicircular portions attached to rectangles or other shapes. Calculate the semicircle area separately using A equals pi r squared divided by 2, then add to the other component areas.
What textbook covers area of semicircles in Grade 7?
Big Ideas Math Advanced 2, Chapter 13: Circles and Area covers the area of semicircles as part of circles and composite figure geometry.