Find the area of a parallelogram if the two sides measure 24.5 inches and 30.9 inches and the shorter diagonal is 30.4 inches. (Round your answer to the nearest whole number.) in2

To find the area of a parallelogram using the lengths of the sides and one diagonal, you can use the formula:

Area = 1/2 * d * √(4a^2 + 4b^2 - d^2)

where a and b are the lengths of the sides and d is the length of the diagonal.

Let's plug in the given values:

Area = 1/2 * 30.4 * √(4*(24.5)^2 + 4*(30.9)^2 - (30.4)^2)

First, calculate the values inside the square root:

= 1/2 * 30.4 * √(4600.25 + 4954.81 - 924.16) = 1/2 * 30.4 * √(2401 + 3819.24 - 924.16) = 1/2 * 30.4 * √(5296.08)

Then, calculate the square root:

= 1/2 * 30.4 * 72.78

Finally, multiply all the values together:

= 1111.5 in^2

Rounding to the nearest whole number, the area of the parallelogram is approximately 1112 square inches.