Question

which figure best demonstrates the setup for the box method of finding the area of a triangle?

Explanation:

The box method (also known as the rectangle method) for finding the area of a triangle involves enclosing the triangle in a rectangle such that the base and height of the triangle correspond to the length and width of the rectangle. The area of the triangle is half the area of this rectangle (since the triangle occupies half of the rectangle's area, as shown by the relationship \( A_{\text{triangle}}=\frac{1}{2} \times \text{base} \times \text{height} \), and \( A_{\text{rectangle}}=\text{base} \times \text{height} \)).

Among the given figures, the second figure (with the red dashed rectangle) encloses the triangle in a rectangle where the triangle’s vertices touch the rectangle’s sides, and the triangle splits the rectangle into two congruent triangles (or shows the correct enclosure for the base - height relationship). The other figures either have incorrect - shaped enclosures (not a rectangle matching the triangle’s base and height) or enclosures that do not properly represent the relationship needed for the box method.

Answer:

The second figure (the one with the red dashed rectangle that fully encloses the triangle with the triangle's vertices touching the rectangle's sides)