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

1 answer

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.