Question

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:

Answer 1

• NK = 7, MK = 2, MF = 9.9, Area = 42

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