# What is the area of a 45-45-90 triangle?

#### Understand the Problem

The question is asking for the area of a 45-45-90 triangle, which is a special type of isosceles right triangle where the angles are 45 degrees. To find the area, we can use the formula for the area of a triangle: Area = (1/2) * base * height. In a 45-45-90 triangle, the base and height are equal, so we can express the area in terms of one of the equal sides.

The area of a 45-45-90 triangle is given by the formula: $$\text{Area} = \frac{1}{2} x^2$$

The area of a 45-45-90 triangle with legs of length $x$ is given by the formula: $$\text{Area} = \frac{1}{2} x^2$$

#### Steps to Solve

1. Identify the sides of the triangle

In a 45-45-90 triangle, the two legs (base and height) are of equal length. Let's denote the length of each leg as $x$.

1. Apply the area formula for a triangle

The formula for the area of a triangle is given by: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$

Since the base and height are both equal to $x$, we can substitute: $$\text{Area} = \frac{1}{2} \times x \times x$$

1. Simplify the area formula

Now, simplify the equation: $$\text{Area} = \frac{1}{2} x^2$$

1. Substitute a specific value for x (if given)

If a specific length for the legs is provided, substitute that value in place of $x$ to calculate the area. For instance, if each leg measures 5 units, then: $$\text{Area} = \frac{1}{2} \times 5^2 = \frac{1}{2} \times 25 = 12.5$$

The area of a 45-45-90 triangle with legs of length $x$ is given by the formula: $$\text{Area} = \frac{1}{2} x^2$$