Semicircle Area Calculator
Calculate the area and perimeter of a semicircle using radius or diameter
Calculate Semicircle Properties
Distance from center to edge
Calculated from radius
Semicircle Results
Formulas used:
- • Area: A = πr²/2 = 0.0000 cm²
- • Perimeter: P = πr + 2r = 0.0000 cm
- • Arc Length: L = πr = 0.0000 cm
- • Diameter: d = 2r = 0.0000 cm
Geometric Properties
Example Calculation
Fireplace Rug Example
Problem: A semicircular rug for a fireplace
Given: Fireplace width = 4 ft (diameter)
Find: Area and perimeter of the semicircular rug
Solution
Step 1: Find radius: r = d/2 = 4/2 = 2 ft
Step 2: Calculate area: A = πr²/2 = π(2)²/2 = 2π ≈ 6.28 ft²
Step 3: Calculate perimeter: P = πr + 2r = 2π + 4 ≈ 10.28 ft
Result: Rug area = 6.28 ft², Lace needed = 10.28 ft
Semicircle Components
Arc
Curved edge = πr
Half the circumference
Diameter
Straight edge = 2r
Forms the base
Radius
Center to edge
Half the diameter
Semicircle Facts
Semicircle area is exactly half a circle's area
Perimeter = curved arc + straight diameter
Every diameter divides a circle into two semicircles
Common in architecture and furniture design
Used in protractors and half-circle windows
Understanding Semicircles
What is a Semicircle?
A semicircle is exactly half of a circle, created when you cut a circle along a diameter line through its center. The prefix "semi-" means half, making this a half-circle. It consists of a curved arc and a straight diameter line.
Semicircle vs Circle
- •Area: Semicircle = ½ × Circle area
- •Perimeter: Semicircle ≠ ½ × Circle circumference
- •The diameter adds extra boundary to the perimeter
Semicircle Formulas
Area: A = πr²/2
Perimeter: P = πr + 2r
Arc Length: L = πr
Real-World Applications
- •Architectural arches and doorways
- •Furniture design (tables, mirrors, rugs)
- •Mathematical instruments (protractors)
- •Food portions (half pizza, watermelon slices)