In an isosceles right triangle, the two equal sides are the legs, and the hypotenuse is opposite the right angle. To find the area of the triangle, we can use the formula for the area of a triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

In an isosceles right triangle, the base and height are the same and correspond to the length of one of the equal sides. In this case, each leg of the triangle is 15 cm.

Thus, the area will be:

$\text{Area} = \frac{1}{2} \times 15 \times 15$ $\text{Area} = \frac{1}{2} \times 225 = 112.5 \, \text{cm}^2$

So, the area of the isosceles right triangle is 112.5 cm².

Let me know if you need further explanation!

Related questions:

1. How do we calculate the hypotenuse of an isosceles right triangle?
2. What is the Pythagorean theorem, and how does it apply to this problem?
3. How do you calculate the area of a triangle if only the hypotenuse is given?
4. How would the area change if the length of the equal sides were different?
5. What is the relationship between the angles and the sides in an isosceles right triangle?

Tip: In an isosceles right triangle, the angles other than the right angle are always 45°.