Question: Find the area of the triangle below.
Be sure to include the correct unit in your answer.
20 cm
21 cm
29 cm
Triangle with a right-angle marker at the top vertex; side lengths are 20 cm on the left, 21 cm on the right, and 29 cm along the bottom base; position_hint=top-left.
1. **State the problem:** We need to find the area of a triangle with side lengths $20$ cm, $21$ cm, and $29$ cm, where the right angle is at the vertex between the sides of lengths $20$ cm and $21$ cm.
2. **Identify the right angle:** Since the triangle has a right angle at the vertex joining the sides $20$ cm and $21$ cm, these two sides are the legs of the right triangle, and the side $29$ cm is the hypotenuse.
3. **Formula for the area of a right triangle:**
$$\text{Area} = \frac{1}{2} \times \text{(leg}_1) \times \text{(leg}_2)$$
4. **Substitute the known values:**
$$\text{Area} = \frac{1}{2} \times 20 \times 21$$
5. **Calculate the area:**
$$\text{Area} = \frac{1}{2} \times 420 = 210$$
6. **Include the unit:** The area is in square centimeters, so the final answer is:
$$\boxed{210\ \text{cm}^2}$$