Note: Figure is not drawn to scale.
If x = 8 units, y = 4 units, and h = 5 units, find the area of the rhombus shown above using decomposition.
A.
13 square units
B.
80 square units
C.
20 square units
D.
40 square units
To find the area of the rhombus, we need to decompose it into two triangles and find the area of each triangle.
The area of a triangle can be calculated using the formula: A = 0.5 * base * height.
For one triangle, with x as the base and h as the height, the area would be:
A1 = 0.5 * 8 * 5 = 20 square units.
Since the rhombus can be divided into two congruent triangles, the total area of the rhombus would be twice the area of one triangle:
Total Area = 2 * 20 = 40 square units.
Therefore, the correct answer is:
D. 40 square units.