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: - NK
- MK
- MF
-

, , ,

Step-by-step explanation:

According to the statement, we find the following inputs:

(Due to the condition of isosceles trapezoid)

Given than longer base and shorter base are parallel to each other, we conclude that:

(By definition of complementary angles)

(Due to the condition of isosceles trapezoid)

(By definitions of complementary and vertical angles and the theorem that states that sum of internal angles within a triangle equals 180º)

(By theorem for 45-45-90 Right Triangle)

(By theorem for 45-45-90 Right Triangle)

If we know that and , then we find that:

The value of MK is obtained from the following relationship:

And the value of KD is calculated from this expression:

Now by the Pythagorean Theorem we find that:

And considering the symmetry characteristics of an isosceles trapezoid, we determine MF:

Lastly, the area of the isosceles trapezoid is determined by the following formula:

If we know that , and , then the area of the figure is:

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