1. What is a 45-45-90 Triangle?

Definition: A special right triangle with two 45° angles and one 90° angle, where both legs are equal in length.

Properties: The hypotenuse is always \( \text{leg} \times \sqrt{2} \), and the area is \( \frac{1}{2} \times \text{leg}^2 \).

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( A \) — Area (square meters)
• \( \text{leg} \) — Length of either equal side (meters)

Explanation: Since both legs are equal, the area is simply half the square of the leg length.

3. Importance of 45-45-90 Triangle Calculations

Applications: Commonly used in construction, engineering, and design for creating square corners and diagonal measurements.

4. Using the Calculator

Tips: Simply enter the length of one leg in meters. The calculator will compute the area in square meters.

5. Frequently Asked Questions (FAQ)

Q1: What if I know the hypotenuse instead of the leg?
A: First calculate the leg length: \( \text{leg} = \text{hypotenuse} \div \sqrt{2} \), then use the calculator.

Q2: Can I use different units?
A: Yes, as long as you're consistent. The result will be in square units of your input (e.g., feet → square feet).

Q3: Why is this triangle special?
A: Its consistent ratios make calculations predictable and it's fundamental in geometry and trigonometry.

Q4: How accurate is this calculator?
A: It provides exact mathematical results based on your input values.

Q5: Can this formula be used for other triangles?
A: No, this specific formula only works for 45-45-90 triangles. Other triangles require different formulas.