In trapezoid ABCD, heights BK and CM are lowered to the larger base AC.

In trapezoid ABCD, heights BK and CM are lowered to the larger base AC. Find the area of the trapezoid if AB = 10, AK = 6, KM = 4, DM = 8.

To find the area of a trapezoid, you need to know the values of the two bases and the height. From the given we calculate that the lower base is 18. The upper base is found from the condition that BK and CM are heights, which means they are perpendicular to the base, therefore KM = BC = 4. It remains to determine the height of the trapezoid.

We find the height of the trapezoid from the triangle ABK, it is rectangular, we can use the Pythagorean theorem. Having written it down, we get BK = 8.

We substitute the trapezoid area into the formula and find the answer.