Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the area of a rhombus given the lengths of the diagonals?

1. A=(1/2)d₁d₂

2. A=d²

3. A=(1/2)b*h

4. A=d₁*d₂

The correct answer is: A=(1/2)d₁d₂

The area of a rhombus can be calculated using the lengths of its diagonals with the formula \( A = \frac{1}{2} d_1 d_2 \), where \( d_1 \) and \( d_2 \) represent the lengths of the diagonals. This formula is derived from the fact that the diagonals of a rhombus bisect each other at right angles, effectively splitting the rhombus into four right triangles. To visualize this, consider that each diagonal creates two triangles. The area of each triangle can be calculated using the base-height formula, but since the diagonals intersect at right angles and bisect each other, the total area can be more easily captured with this diagonal formula. When you take half of each diagonal and multiply them together, and then multiply by 2 (for the two triangles created by one diagonal), the result is a straightforward method to derive the total area of the rhombus. The other provided formulas do not correctly capture the area based on the diagonals of the rhombus. The formula involving \( d^2 \) represents an area that is not applicable here. The formula \( A = \frac{1}{2} b h \)