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

Definition: This calculator computes the area of an isosceles right triangle (45-45-90 triangle) based on the length of its legs.

Purpose: It helps students, architects, and construction professionals quickly determine the area of this special right triangle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( A \) — Area of the triangle (square meters)
• \( \text{leg} \) — Length of the equal sides (meters)

Explanation: In a 45-45-90 triangle, the two legs are equal, and the area is simply half the square of one leg's length.

3. Importance of 45-45-90 Triangle Calculation

Details: These special triangles are common in construction, design, and geometry problems. Knowing their properties simplifies many calculations.

4. Using the Calculator

Tips: Simply enter the length of one leg in meters. The value must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a 45-45-90 triangle?
A: It's an isosceles right triangle where the two legs are equal and the angles are 45°, 45°, and 90°.

Q2: What's the relationship between the legs and hypotenuse?
A: The hypotenuse is always \( \text{leg} \times \sqrt{2} \) in length.

Q3: Can I use this for other triangles?
A: No, this formula only works for 45-45-90 triangles. Other triangles require different formulas.

Q4: Why is the area half the square of the leg?
A: Because in a right triangle, the area is always (1/2) × base × height, and in this case base = height = leg.

Q5: What units should I use?
A: The calculator uses meters, but the formula works with any unit as long as you're consistent.