Find the length of each diagnol and the area

Mathematics

1 answer:

katrin [286]3 years ago

7 0

Answer:

The length of diagonal BD is 11·(1 + √3)

The length of diagonal AC = 22

Step-by-step explanation:

The given data are;

Quadrilateral ABCD = A kite

The length of segment AD = 22

The measure of ∠DAE = 60°

The measure of ∠BCEE = 45°

Whereby, triangle ΔADE = A right triangle, and DE is the perpendicular bisector of AC, by trigonometric ratio, we have;

AE = EC

DE = 22 × sin(60°) = 11·√3

AE = 22 × cos(60°) = 11

∴ AE = EC = 11

BE = EC × tan(∠BCE) = 11 × tan(45°) = 11

The length of the diagonal BD = BE + DE (By segment addition property)

∴ BD = 11 + 11·√3 = 11·(1 + √3)

The length of diagonal BD = 11·(1 + √3)

The length of diagonal AC = AE + EC

∴ AC + 11 + 11 = 22

The length of diagonal AC = 22.

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