Final answer:
To determine the height of a trapezoid with an area of 36 square yards and bases of 5 and 7 yards, use the trapezoid area formula, resulting in a height of 6 yards.
Step-by-step explanation:
To find the height of a trapezoid when given the area and the lengths of its bases, you can use the formula for the area of a trapezoid, which is A = \((b_1 + b_2)/2\) \times h, where A is the area, \(b_1\) and \(b_2\) are the lengths of the two bases, and h is the height. Given that the area is 36 square yards, and the bases are 5 yards and 7 yards, the equation can be set up as 36 = \((5 + 7)/2\) \times h. Simplifying this, we get 36 = 6 \times h, and by dividing both sides by 6, we find that the height is 6 yards.
The formula for the area of a trapezoid is given by:
Area = (base1 + base2) × height ÷ 2