The MT and KP bases of the MKPT trapezoid are 14 and 6 dm, respectively.

The MT and KP bases of the MKPT trapezoid are 14 and 6 dm, respectively. The area of the triangle MKT is 28 dm2. Calculate the area of this trapezoid.

Consider the MKT triangle. Its height KN, drawn from the top K to the side of MT, coincides with the height of the MCRT trapezium. Knowing that the area of a triangle is equal to half the product of the length of a side by the height drawn to this side, we can write:

SMKT = 0.5 * MT * KH.

From here we find the height: KH = 2 * SMKT / MT = 2 * 28/14 = 4 dm.

The area of the trapezoid is equal to the product of the half-sum of the bases and the height of the trapezoid:

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