Area of a Semicircle
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 13: Circles and Area) learn the area formula for a semicircle: A = pi r squared / 2. This is half the area of the full circle, applied to composite figures containing semicircular regions such as arched windows and semicircular gardens.
Key Concepts
Property A semicircle is exactly half of a full circle. To find its area, calculate the area of the full circle first, and then simply divide by 2: $$A = \frac{\pi r^2}{2}$$.
Examples Find the area of a semicircle with a radius of 6 cm. Full circle area is $36\pi$. Semicircle area is $36\pi / 2 = 18\pi$ square cm (about 56.52 square cm). A semicircular window has a diameter of 8 feet. First, find the radius (4 feet). Full circle area is $16\pi$. Semicircle area is $16\pi / 2 = 8\pi$ square feet.
Explanation Don't let semicircles trick you! There is no need to memorize a completely new, complicated formula. Just pretend it is a perfectly normal, full circle, do your standard $\pi r^2$ math, and at the very end, chop your answer in half.
Common Questions
What is the formula for the area of a semicircle in 7th grade?
A = (pi x r squared) / 2. Calculate the full circle area (pi r squared) then divide by 2.
How do you find the area of a semicircle with radius 6 cm?
Full circle: pi x 36 = 36 pi. Semicircle: 36 pi / 2 = 18 pi approximately 56.52 square cm.
What if you are given the diameter instead of the radius?
Divide the diameter by 2 to get the radius, then apply A = pi r squared / 2. For a diameter of 8 feet, radius = 4 feet, area = pi x 16 / 2 = 8 pi square feet.
What chapter in Big Ideas Math Advanced 2 covers area of semicircles?
Chapter 13: Circles and Area in Big Ideas Math Advanced 2 (Grade 7) covers area of semicircles.
What is the shortcut for semicircle area?
Calculate full circle area normally with A = pi r squared, then halve the result. No need to memorize a separate formula.