Final answer:
To find the height of a trapezoid with a known area, rearrange the trapezoid area formula to solve for height.
Step-by-step explanation:
To find the height of a trapezoid when the area is known, you can rearrange the formula for the area of a trapezoid, which is A = (a + b) / 2 × h, where A is the area, a and b are the lengths of the parallel sides, and h is the height. If you know the area and the lengths of the parallel sides, you can solve for the height h using the formula h = 2A / (a + b).
For example, if you're given a question about the area of a triangle using the formula A = 1/2 × base × height, you can use similar steps to solve for the height if the base and area are known. Let's consider a triangle with a base of 166 mm and an area of 77085 square millimeters (since area is in square units, make sure your base and height are in the same units). You would use the formula rearranged to height = 2 × A / base. Plugging in the numbers, height = 2 × 77085 mm² / 166 mm = 930 mm.
Always ensure that you use the same units for all measurements and express your final answer to the proper number of significant figures, usually determined by the precision of the given values in the problem.