The bases МТ and KР of the trapezoid МKPТ are equal to 14 dm and 6 dm, respectively.

The bases МТ and KР of the trapezoid МKPТ are equal to 14 dm and 6 dm, respectively. The area of the MKT triangle is 28 dm ^ 2. Calculate the area of this trapezoid.

The area of the MKT triangle is equal to half the product of the side MT by the height drawn to it from the vertex K:

SMKT = 0.5 * MT * h.

Hence:

h = 2 * SMKT / MT = 2 * 28/14 = 4 in.

The height of the MKT triangle, drawn to the side of the MT, coincides with the height of the MKRT trapezium. The area of the trapezoid is equal to the product of the length of the height and half of the sum of the lengths of the bases:

SMKPT = h * (MT + KP) / 2 = 4 * (14 + 6) / 2 = 20 * 2 = 40 dm2.