Sector Area Calculator

This Sector Area Calculator helps you find the area of a sector when the radius and central angle are known. It first converts the angle from degrees to radians, then uses the formula A = \(\frac{1}{2}\)r²θ, where r is the radius and θ is the angle in radians. Square the radius, multiply by the angle in radians, and then multiply by \(\frac{1}{2}\) to get the sector area. It is a simple way to check answers, understand sector area formulas, and practise basic trigonometry step by step.

Step-by-step method

1. Identify what is given.
2. Convert the angle from degrees to radians.
3. Use the sector area formula.
4. Substitute and calculate.

Formulas:

Formula: degrees to radians

Formula: sector area

Example 1: r = 4, θ = 60°

Step 1 - Identify what is given.

In this problem: The given values are r = 4 and θ = 60°.

Step 2 - Convert the angle from degrees to radians.

In this problem: Convert degrees to radians using θ(rad) = θ(°) × π / 180.

Step 3 - Use the sector area formula.

In this problem: Use the sector area formula A = ½ × r² × θ(rad).

Step 4 - Substitute and calculate.

In this problem: Substitute and calculate the area: A = 8.37758041.

Final answer: A = 8.37758041

Example 2: r = 5.5, θ = 120°

Step 1 - Identify what is given.

In this problem: The given values are r = 5.5 and θ = 120°.

Step 2 - Convert the angle from degrees to radians.

In this problem: Convert degrees to radians using θ(rad) = θ(°) × π / 180.

Step 3 - Use the sector area formula.

In this problem: Use the sector area formula A = ½ × r² × θ(rad).

Step 4 - Substitute and calculate.

In this problem: Substitute and calculate the area: A = 31.67772592.

Final answer: A = 31.67772592