Final answer:
The area of a rhombus can be found by splitting it into two congruent right triangles and using the formula for the area of a triangle. The total area of the rhombus is twice the area of one right triangle.
Step-by-step explanation:
A rhombus is a quadrilateral with all four sides equal in length. In a rhombus, diagonals bisect each other at right angles, which means that a rhombus can always be split into four congruent right triangles. The area of a triangle can be found using the formula: Area = 1/2 × base × height.
Since the diagonal measures 10 cm and at least one angle is 90°, we can split the rhombus into two congruent right triangles. One of the right triangles will have legs measuring 5 cm and 10 cm. Therefore, the area of one right triangle is:
Area = 1/2 × base × height = 1/2 × 5 cm × 10 cm = 25 cm²
Since the rhombus consists of two congruent right triangles, the total area of the rhombus is twice the area of one right triangle:
Total Area = 2 × 25 cm² = 50 cm²