In parallelogram ABCD, point K is the midpoint of side AD. Find the area of a parallelogram

In parallelogram ABCD, point K is the midpoint of side AD. Find the area of a parallelogram if the area of the triangle DCK is 5.

Let the side of the parallelogram be AD = a, and the side DC = b.

Then KD = a / 2.

The area of the triangle KDC can be calculated using the formula:

S (KDC) = 1/2 * KD * DC * sinD

S (KDC) = 1/4 * a * b * sinD

The parallelogram area can be calculated using the formula:

S (ABCD) = AD * DC * sinD = a * b * sin D

If we divide this expression by the expression for the area of the triangle KDC, we get the proportion from which it is convenient to find the unknown area of the parallelogram. a and b are canceled in this case.

S (ABCD) = 4 * S (KDC) = 4 * 5 = 20

Answer: S (ABCD) = 20.