In the KMNP trapezoid, the angle is M-straight, the base NP is 4cm.

In the KMNP trapezoid, the angle is M-straight, the base NP is 4cm. The MKR triangle is rectangular and isosceles. Find the area of the trapezoid.

Let’s construct the height of the PH trapezoid.
Since the MRK triangle is rectangular and isosceles, then the RN is the median of the triangle.
The length of the segment MH = NP = 4 cm, then MK = 2 * MH = 2 * 4 = 8 cm.
The MRN triangle is rectangular and isosceles, since the PH is the height, and the angle is PMN = MRN = 450.
Then RH = MH = 4 cm.
The area of the trapezoid will be equal to: Strap = (NP + MK) * PH / 2 = (4 + 8) * 4/2 = 12 * 2 = 24 cm2.
Answer: The area of the trapezoid is 24 cm2.