In ΔDEF, e = 130 inches, f = 130 inches and ∠D=57°. Find the area of ΔDEF, to the nearest square inch.

To find the area of a triangle given two sides and the included angle, you can use the formula:

Area = 1/2 * a * b * sin(C)

In this case, a and b are the lengths of the sides (e and f), and C is the included angle (∠D).

So,

Area = 1/2 * e * f * sin(∠D) = 1/2 * 130 inches * 130 inches * sin(57°) = 1/2 * 16900 inches^2 * sin(57°)

Now, we need to calculate the sine of 57 degrees. Using a calculator, sin(57°) is approximately 0.83867.

So,

Area = 1/2 * 16900 inches^2 * 0.83867 = 7089.815 inches^2

Rounding to the nearest square inch, the area of ΔDEF is approximately 7090 square inches.