Final answer:
To find the area of trapezoid WXYZ, it is necessary to calculate the height using the Pythagorean theorem on the right triangle formed by the non-parallel sides and one of the parallel sides, then apply the area formula for trapezoids. Substituting the given lengths, the calculated area 152 square units does not match the provided options, indicating a potential error in the given data or the calculations.
Step-by-step explanation:
To find the area of trapezoid WXYZ, with WX parallel to YZ, we can split it into a rectangle and a right triangle. The length of WX is 17 units and the length of YZ is 21 units. The difference between these two lengths, which will serve as the height of the right triangle part, is 21 - 17 = 4 units.
Using the Pythagorean theorem in the right triangle ∆WXY, where XY = 13 units and WX = 17 units (height of the rectangle), we can find the height of the trapezoid (right triangle's other leg). The Pythagorean theorem states that c² = a² + b², where c is the hypotenuse. Therefore, 13² = h² + 17² and by calculating h² = 13² - 17², we find h to be 8 units, which is also the height of the trapezoid.
The area of the trapezoid is given by A = ½ * (sum of parallel sides) * height, which translates to A = ½ * (17 + 21) * 8, which yields an area of 152 square units. However, this is not an option in the given choices, so it is important to revisit the calculations or the given information to ensure accuracy.