Given an MNKP trapezoid, angle M = 45 degrees, angle P = 30 degrees, MN = 8cm, KP = 10cm

| September 11, 2021 | education

Given an MNKP trapezoid, angle M = 45 degrees, angle P = 30 degrees, MN = 8cm, KP = 10cm, NK = 5cm Find the middle line.

From the vertices obtuse angle N and K, we omit two heights NH and KB.

In a right-angled triangle MNH, by the Pythagorean theorem, we define the length of the leg MN.

MH = MN * Cos450 = 8 * √2 / 2 = 4 * √2 cm.

In a right-angled triangle KPV, according to the Pythagorean theorem, we determine the length of the leg PB.

РВ = КР * Cos300 = 10 * √3 / 2 = 5 * √3 cm.

The quadrilateral NKVN is a rectangle, since NP is parallel to HB as the base of the trapezoid, and NH is parallel to KB as the height of the trapezoid, then HB = NK = 5 cm.

Let us determine the length of the base of the MP. МР = НВ + МН + РВ = 4 * √2 + 5 + 5 * √3 ≈ 19.32 cm.

Determine the length of the midline of the trapezoid.

SD = (NK + MP) / 2 = (5 + 19.32) / 2 = 12.16 cm.

Answer: The length of the middle line is 12.16 cm.



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