Question

How can the area of this triangle be determined by forming a rectangle? Select from the drop-down menus to correctly complete the statements. Copy and rotate the triangle and place it next to the existing triangle to form a rectangle. The length of the rectangle is Choose... units. The width of the rectangle is Choose... units. The area of the rectangle is Choose... square units. The area of the triangle is half the area of the rectangle, so the area of the triangle is Choose... square units. Right triangle on a grid. One side of the triangle is horizontal and has a length of 13 units. Another side is vertical and has a length of 2 units.

Answer 1

The length of the rectangle is 13 units.

The width of the rectangle is 2 units.

The area of the rectangle is 26 square units.

The area of the triangle is half the area of the rectangle, so the area of the triangle is 13 square units.

To form the rectangle, we copy the given right triangle and rotate it 90 degrees so that its vertical side is aligned with the horizontal side of the original triangle. The two triangles together form a rectangle, where one side of the rectangle is the horizontal side of the original triangle with a length of 13 units, and the other side of the rectangle is the vertical side of the original triangle with a length of 2 units. Therefore, the length of the rectangle is 13 units and the width of the rectangle is 2 units. The area of the rectangle is the product of the length and width, which is 26 square units. Since the triangle is half of the rectangle, its area is half of 26 square units, or 13 square units.

Answer 2

To determine the area of the triangle by forming a rectangle, we can copy and rotate the triangle and place it next to the existing triangle to form a rectangle. The length of the rectangle is 13 units. The width of the rectangle is 2 units. The area of the rectangle is 26 square units. The area of the triangle is half the area of the rectangle, so the area of the triangle is 13 square units.