Answer:
a = 35.68 sq. units
Explanation:
The area of a rhombus can be found by multiplying the lengths of its diagonals and dividing by 2:
Area = (diagonal 1 x diagonal 2) / 2
However, we are not given the diagonals of the rhombus. Instead, we are given that one of its sides, y, is 12 units, and its height, h, is 8 units.
Since a rhombus has four equal sides, we know that the length of the other side must also be 12 units. Therefore, the length of both diagonals of the rhombus can be found using the Pythagorean theorem:
diagonal = √(side^2 + height^2)
diagonal = √(12^2 + 8^2)
diagonal = √(144 + 64)
diagonal = √208
diagonal ≈ 14.4222 units
Now that we know the lengths of both diagonals, we can use the formula for the area of a rhombus:
Area = (diagonal 1 x diagonal 2) / 2
Area = (12 units x √208 units) / 2
Area ≈ 35.68 square units
Therefore, the area of the rhombus is approximately 35.68 square units.