MKNP is a trapezoid. NK and MP bases. NK refers to MP as 3: 5. The area of the trapezoid is 104.

MKNP is a trapezoid. NK and MP bases. NK refers to MP as 3: 5. The area of the trapezoid is 104. Find the area of the triangle MNK.

Let the base KN = 3 * X, then MP = 5 * X.

The area of the triangle MKN will be equal to: Smkn = KN * KA / 2 = 3 * X * KA / 2.

The area of the triangle МНР will be equal to: Smnr = МР * KA / 2 = 5 * X * KA / 2. Let’s find the ratio of the areas of the triangles.

Smcn / Smnr = (3 * X * KA / 2) / (5 * X * KA / 2) = 3/5.

5 * Smnr / 3 = Smnr.

Smcn + Smnr = Smcnr = 104.

Smcn = 104 – Smnr = 104 – 5 * Smcn / 3.

8 * Smcn / 3 = 104.

Smcn = 104 * 3/8 = 39 cm2.

Answer: The area of the MKH triangle is 39 cm2.