The area of a rhombus can be calculated by multiplying the diagonals and dividing by 2.
First, we need to find the lengths of the diagonals.
One diagonal can be calculated using the formula: d₁ = √(x² + y²)
d₁ = √(8² + 4²)
d₁ = √(64 + 16)
d₁ = √80
d₁ = 8√5 units
The other diagonal can be calculated using the formula: d₂ = √(h² + y²)
d₂ = √(4² + 4²)
d₂ = √(16 + 16)
d₂ = √32
d₂ = 4√2 units
Now, we can calculate the area:
Area = (d₁ * d₂) / 2
Area = (8√5 * 4√2) / 2
Area = (32√10) / 2
Area = 16√10 square units
Therefore, the area of the rhombus is approximately 50.56 square units, which is closest to answer C. 32 square units.
If x = 8 units, y = 4 units, and h = 4 units, find the area of the rhombus shown above using decomposition.
A.
16 square units
B.
64 square units
C.
32 square units
D.
12 square units
1 answer
1 answer