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?
A) 21 square units
B) 10.5 cubic units
C) 10.5 units
D) 10.5 square units
To model the area formula of Triangle C, we can decompose it into a rectangle and two right triangles.
The rectangle formed by Triangle C is 5 units by 9 units, so its area is 5 x 9 = 45 square units.
Each right triangle formed by Triangle C has a base of 5 units and a height of 9 units, so its area is 0.5 x 5 x 9 = 22.5 square units for both right triangles combined.
Adding the area of the rectangle and the area of the two right triangles gives us the total area of Triangle C:
45 square units + 22.5 square units = 67.5 square units
Therefore, the area of Triangle C is 67.5 square units, which is closest to option A) 21 square units.