What is the area of a rhombus with diagonals measuring 4 centimeters and 7 centimeters?

• A. 28 square centimeters
• B. 14 square centimeters
• C. 8 square centimeters
• D. 10 square centimeters

Answer: (B)

To find the area of a rhombus when the lengths of the diagonals are known, the formula used is:

[

\text{Area} = \frac{d_1 \times d_2}{2}

]

where (d_1) and (d_2) are the lengths of the diagonals. In this case, the diagonals measure 4 centimeters and 7 centimeters.

Substituting the values into the formula:

[

\text{Area} = \frac{4 \times 7}{2} = \frac{28}{2} = 14 \text{ square centimeters}

]

Thus, the area of the rhombus is 14 square centimeters, confirming that this is indeed the correct answer. This formula works because the diagonals of a rhombus bisect each other at right angles, leading to two triangles that each have half the area determined by the product of the diagonals.