Question

note: figure is not drawn to scale. if x = 4 units, y = 6 units, and h = 6 units, find the area of the rhombus shown above using decomposition.

Explanation:

Step1: Decompose the rhombus

Split the rhombus into 2 congruent triangles and 1 rectangle.

Step2: Calculate rectangle area

Area of rectangle: $x \times h = 4 \times 6 = 24$

Step3: Calculate triangle base length

Base of one triangle: $\frac{y - x}{2} = \frac{6 - 4}{2} = 1$

Step4: Calculate one triangle area

Area of 1 triangle: $\frac{1}{2} \times 1 \times 6 = 3$

Step5: Calculate total triangle area

Area of 2 triangles: $2 \times 3 = 6$

Step6: Sum all areas for total

Total area: $24 + 6 = 36$

Answer:

36 square units