Amaury draws an acute triangle on the coordinate grid. He finds the area of the triangle by drawing a rectangle that circumscribes the triangle and forming right triangles. How can Amaury find the area of the triangle? What is the area of the triangle in square units?
To find the area of the triangle, Amaury can use the formula for the area of a triangle, which is $\frac{1}{2} \times \text{base} \times \text{height}$.
In this case, Amaury can use the sides of the rectangle that circumscribes the triangle as the base and height. The base of the triangle is the length of the rectangle, and the height of the triangle is the width of the rectangle.
Since the triangle is acute, Amaury can draw perpendicular lines from the vertices of the triangle to the sides of the rectangle. This will create right triangles within the rectangle.
By using the Pythagorean Theorem to find the lengths of the perpendiculars, Amaury can determine the base and height of the triangle. Then, by plugging in these values into the formula for the area of a triangle, he can calculate the area.
The area of the triangle will be expressed in square units, which will depend on the specific units used on the coordinate grid.
Note: Without further information about the specific points on the coordinate grid or the lengths of the sides of the rectangle, it is not possible to determine the area of the triangle.