Use decomposition and rearranging to model the area formula of triangle C. What is the area of triangle C in square units? (1 point)
20 units
20 square units
80 square units
40 square units
To find the formula for the area of triangle C, we can decompose it into two smaller triangles and rearrange them to form a rectangle.
Let the base of triangle C be x units and the height be 2x units.
The area of the two smaller triangles is:
Triangle 1: 1/2 * x * 2x = x^2 square units
Triangle 2: 1/2 * (4x - x) * 2x = 3x^2 square units
When we rearrange them to form a rectangle, we get:
Width = 4x units
Height = 2x units
The area of the rectangle is:
4x * 2x = 8x^2 square units
Since the area of the rectangle is equal to the sum of the areas of the two smaller triangles, we have:
8x^2 = x^2 + 3x^2
8x^2 = 4x^2
4x^2 = 80
Therefore, the area of triangle C is 80 square units.
Correct answer: 80 square units