Calculate the area of a half-circle
Step 1: Measure the Radius or Diameter
Obtain either the radius (from center to edge) or diameter (straight across through center).
Why: These linear measurements are the foundation for all area calculations.
Step 2: Ensure Consistent Units
Verify all measurements use the same unit (cm, m, inches, etc.).
Why: Mixed units produce incorrect areas; result also becomes unit².
Step 3: Calculate or Verify the Radius
If given diameter d, compute r = d/2. If given r, proceed directly.
Why: The formula requires radius; diameter must be converted first.
Step 4: Apply the Semicircle Formula
Use A = (π × r²) / 2 or equally A = (1/2) × π × r².
Why: This formula explicitly represents half of a full circle’s area (πr²).
Step 5: Round and Check Reasonableness
Round to appropriate precision and verify the area is positive and exactly half the full circle area.
Why: Catching errors early prevents downstream calculation mistakes.
A semicircle is exactly half of a circle. Its area is half the area of a full circle:
A = (π × r²) / 2Where r is the radius of the semicircle.