Use decomposition and rearranging to model the area formula of triangle C. What is the area of triangle C in square units?

10.5 cubic units
10.5 units
10.5 square units * MY ANSWER IS IT CORRECT
21 square units

1 answer

To find the area of triangle C, we need to use the formula for the area of a triangle:

Area = 1/2 * base * height

Let's decompose the triangle into two right triangles by drawing a line from vertex A perpendicular to side BC (let's call the point where the line crosses side BC point D).

Now, triangle C is composed of two right triangles: triangle ABD and triangle ACD.

The base of triangle ABD is 5 units (from B to D) and the height is 2 units (from A to D).

The area of triangle ABD is:
1/2 * 5 * 2 = 5 square units

Similarly, the base of triangle ACD is 7 units (from C to D) and the height is 3 units (from A to D).

The area of triangle ACD is:
1/2 * 7 * 3 = 10.5 square units

Therefore, the total area of triangle C is the sum of the areas of triangles ABD and ACD, which is 5 + 10.5 = 15.5 square units.

So, the correct answer is: 10.5 square units.