Use the image to answer the question.

Question

An illustration shows a 5 by 9 grid labeled Triangle C. Triangle C is graphed on the grid.
Use decomposition and rearranging to model the area formula of triangle C . What is the area of triangle C in square units?(1 point)
Responses

10.5 units
10.5 units

10.5 cubic units
10.5 cubic units

10.5 square units
10.5 square units

21 square units

Answer 1

To find the area of Triangle C, we can decompose the triangle into two smaller right triangles and a larger rectangle.

Let x represent the base of the triangle, and y represent the height of the triangle. The rectangle has a width of x units and a length of y units.

The total area of Triangle C can be represented as:

Area of Triangle C = Area of Rectangle + 2(Area of Right Triangle)

Area of Triangle C = xy + 2(1/2 * (x/2) * y)

Area of Triangle C = xy + x * y

Area of Triangle C = 2xy

Now, look at the grid and write down the coordinates of the triangle. Count the number of whole units inside the triangle and calculate the area.

Based on the grid provided, the area of Triangle C is 10.5 square units.