A rhombus has a diagonal with a length of 17 ft. and a side measurement of 9.5 ft. What is the area of the rhombus?

To find the area of the rhombus, we need to use the formula: Area = (Product of the diagonals) / 2.

In this case, we are given the length of one diagonal (17 ft.), but we need to find the length of the other diagonal. Since the opposite angles of a rhombus are congruent, we can use the Pythagorean theorem to find the length of the other diagonal.

Let's call the other diagonal x. We know that one side of the rhombus is 9.5 ft., and since opposite sides of a rhombus are congruent, the other side is also 9.5 ft. Thus, we can form a right triangle with one leg being half of one side (4.75 ft.), and the other leg being half the length of the other diagonal (x/2).

Using the Pythagorean theorem, we have:

(4.75 ft.)^2 + (x/2)^2 = (9.5 ft.)^2

Solving for x, we get:

22.5625 ft. + (x/2)^2 = 90.25 ft.

(x/2)^2 = 67.6875 ft.

x/2 = sqrt(67.6875) ft.

x = 2 * sqrt(67.6875) ft.

Now that we have the lengths of both diagonals, we can substitute them into the formula to find the area:

Area = (17 ft. * 2 * sqrt(67.6875) ft.) / 2

Area = 17 ft. * sqrt(67.6875) ft.

Area ≈ 17 ft. * 8.232 ft.

Area ≈ 139.944 sq. ft.

Therefore, the area of the rhombus is approximately 139.944 square feet.