Question: Calculate the area of this triangle.
Diagram not to scale
5 cm
13 cm
12 cm
Right triangle in the center-left of the page with a vertical left side labeled 5 cm, a horizontal base labeled 12 cm, and a slanted side labeled 13 cm; position_hint = center.
1. **State the problem:** We need to find the area of a right triangle with legs of lengths $5$ cm and $12$ cm, and a hypotenuse of $13$ cm.
2. **Formula:** The area $A$ of a right triangle is given by:
$$A = \frac{1}{2} \times \text{base} \times \text{height}$$
3. **Identify base and height:** Since the triangle is right-angled, the legs $5$ cm and $12$ cm serve as the base and height.
4. **Calculate the area:**
$$A = \frac{1}{2} \times 12 \times 5$$
5. **Simplify:**
$$A = \frac{1}{2} \times 60$$
6. **Final answer:**
$$A = 30$$ cm$^2$
The area of the triangle is $30$ square centimeters.