Question

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?

Answer 1

To find the area of the triangle, Amaury can draw a rectangle that circumscribes the triangle. Then, he can draw two diagonal lines inside the rectangle to form right triangles. The hypotenuses of these right triangles will be the two sides of the triangle that are not the base.

Amaury can find the lengths of these two sides by subtracting the x-coordinates and y-coordinates of the triangle's vertices. Let's say the triangle's vertices are (x1, y1), (x2, y2), and (x3, y3). The length of one side would be √((x2 - x1)^2 + (y2 - y1)^2), and the length of the other side would be √((x3 - x1)^2 + (y3 - y1)^2).

Once Amaury has the lengths of the two sides, he can multiply them together and divide by 2 to find the area of the triangle.

To find the area of the triangle in square units, Amaury would need the specific coordinates of the triangle's vertices. Without that information, it is not possible to determine the area of the triangle.