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URGENT HELP!!
The angle between a diagonal and the longer base of the isosceles trapezoid MNFD is 45°. NK is an altitude to the longer base. If MD = 9 and NF = 5, find:

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mhanifa

Answer:

  • NK = 7, MK = 2, MF = 9.9, Area = 42

Step-by-step explanation:

Refer to attached

To find:

  • NK ,  MK,  MF, Area of trapezoid

Solution

The trapezoid is isosceles and NK is its height, therefore

  • MD - NF = 2MK
  • MK = (9 -5)/2 = 2

Since ∠KDN = 45°, the triangle NKD is isosceles and so

  • NK = KD = MD - MK = 9 - 2 = 7

MF  = ND as trapezoid is isosceles and therefore diagonals are equal

  • ND = NK√2 = 7√2 = 9.9
  • So MF = 9.9

Area of trapezoid

  • A = 1/2(b1 + b2)h
  • A = 1/2(9+5)(7) = 6*7 = 42
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