In ΔQRS, r = 140 inches, s = 270 inches and ∠Q=102°. Find the area of ΔQRS, 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 * r * s * sin(Q)

where r and s are the lengths of the two sides, and Q is the included angle.

Step 1: Convert the angle from degrees to radians. In this case, Q = 102° = 102 * π/180 = 1.78 radians.

Step 2: Substitute the values into the formula:

Area = 1/2 * 140 inches * 270 inches * sin(1.78 radians)

Step 3: Calculate the area:

Area = 1/2 * 140 * 270 * sin(1.78) = 1/2 * 140 * 270 * 0.9781 = 18515.94 square inches

So, the area of ΔQRS is approximately 18516 square inches, to the nearest square inch.