Final answer:
The area of a rhombus with one side of 9 ft is 162 square feet.
Step-by-step explanation:
The area of a rhombus can be found by multiplying the lengths of its diagonals and dividing by 2. However, since only one side is given, we can find the area using a different formula. A rhombus can be divided into four congruent right triangles, so the area of the rhombus is equal to four times the area of one of these triangles. The base of the triangle is half the length of one side of the rhombus, and the height can be found using the Pythagorean Theorem.
Let's say the length of one side of the rhombus is 9 ft. Then the base of the right triangle would be 9/2 ft. Using the Pythagorean Theorem, we can find the height of the triangle. Since the rhombus is a square, the height is also the length of one of the diagonals, which is 9 ft.
So, the area of one right triangle is (9/2) * 9 = 81/2 square feet. Multiplying this by 4 gives us the area of the rhombus, which is 162 square feet.