Each of the two equal sides of an isosceles right triangle is 10cm long. Its area is

1. ### Break Down the Problem

To find the area of an isosceles right triangle where the two equal sides are 10 cm each, we need to:

1. Identify the formula for the area of a triangle.
2. Apply the specific properties of an isosceles right triangle.

2. ### Relevant Concepts

The formula for the area $A$ of a triangle is given by: $A = \frac{1}{2} \times \text{base} \times \text{height}$ For an isosceles right triangle, the two equal sides can be considered as the base and height.

3. ### Analysis and Detail

In this case:

• Both the base and the height are equal to the lengths of the sides, which is 10 cm.

Substituting the values into the formula: $A = \frac{1}{2} \times 10 \, \text{cm} \times 10 \, \text{cm}$ $A = \frac{1}{2} \times 100 \, \text{cm}^2$ $A = 50 \, \text{cm}^2$

4. ### Verify and Summarize

The calculations have been performed correctly to find the area of an isosceles right triangle with side lengths of 10 cm. Thus, the area is confirmed.

Final Answer

The area of the triangle is $50 \, \text{cm}^2$.