Question: Work out the area of this triangle.
10 cm
7 cm
6 cm
15 cm
Not to scale
Shape: a green scalene triangle inside a dashed rectangle; the triangle has a top-left vertex, a bottom-middle vertex, and a bottom-right vertex, with the 10 cm label on the left slanted side, 7 cm on the bottom side, 6 cm on the right vertical height, and 15 cm along the bottom of the dashed rectangle; position_hint=center
1. **State the problem:** We need to find the area of a scalene triangle with a base of $7$ cm and a height of $6$ cm.
2. **Formula for the area of a triangle:**
$$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$
3. **Identify the base and height:**
- Base $= 7$ cm (bottom side of the triangle)
- Height $= 6$ cm (vertical height from the base to the opposite vertex)
4. **Substitute the values into the formula:**
$$\text{Area} = \frac{1}{2} \times 7 \times 6$$
5. **Calculate the multiplication:**
$$\text{Area} = \frac{1}{2} \times 42$$
6. **Simplify the fraction:**
$$\text{Area} = \cancel{\frac{1}{2}} \times \cancel{42} = 21$$
7. **Final answer:**
The area of the triangle is $21$ square centimeters.