Question: What is the area of the triangle below?
Triangle shape in the center of the graph; its vertices are approximately at top-center, bottom-left, and right-middle, and it is drawn on a square grid.
units²
1. **State the problem:** We need to find the area of a triangle given its vertices on a coordinate grid.
2. **Identify the vertices:** From the description, the triangle's vertices are approximately at top-center, bottom-left, and right-middle of the grid. Let's assign coordinates:
- Top-center: $A(5,10)$
- Bottom-left: $B(0,0)$
- Right-middle: $C(10,5)$
3. **Formula for the area of a triangle given coordinates:**
$$\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|$$
4. **Plug in the coordinates:**
$$\text{Area} = \frac{1}{2} |5(0 - 5) + 0(5 - 10) + 10(10 - 0)|$$
5. **Calculate inside the absolute value:**
$$= \frac{1}{2} |5(-5) + 0(-5) + 10(10)|$$
$$= \frac{1}{2} |-25 + 0 + 100|$$
$$= \frac{1}{2} |75|$$
6. **Simplify:**
$$= \frac{1}{2} \times 75$$
$$= 37.5$$
7. **Final answer:** The area of the triangle is $37.5$ square units.