If x = 9 units, y = 3 units, and h = 8 units, find the area of the rhombus shown above using decomposition.
A.
24 square units
B.
128 square units
C.
72 square units
D.
16 square units
To find the area of the rhombus, we need to first decompose it into two triangles and find the area of one of the triangles, then multiply by 2.
Each triangle within the rhombus can be formed by the diagonal lengths x and y, with the height h as one of the sides. The area of a triangle can be calculated using the formula:
Area = 0.5 * base * height
In this case, the base is the diagonal length x = 9 units and the height is h = 8 units. Substituting the values into the formula:
Area of one triangle = 0.5 * 9 * 8 = 36 square units
Since there are two triangles in the rhombus, the total area of the rhombus is:
Total area = 2 * 36 = 72 square units
Therefore, the correct answer is:
C. 72 square units