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I cannot draw the rhombus using this keyboard.

I have rhombus ABCD. Angle A = 40 degrees and diagonal AC = 20.

I tried using trig to find diagonal BD but was not able to.

How do I find the area of this rohombus given the data above?

Thanks

2007-08-09 10:04:46 · 2 answers · asked by journey 1 in Science & Mathematics Mathematics

2 answers

Diagonals bisect each other.
Let diagonals bisect at E
In triangle ABE:-
Angle A = 40°
AE = 10
tan 40° = BE / 10
BE = 10 tan 40°
BE = 8.39
Diagonal BD = 16.78
Area = (1/2) x (16.78) x (20)
Area = 167.8 units ²

2007-08-09 10:52:17 · answer #1 · answered by Como 7 · 1 0

The diagonals of a rhombus intersect at right angles, and bisect each other. Adjacent sides are equal.
Therefore AP = 10, angle DAP = 20deg, and AB = AD.

Let the point of intersection of the diagonals be P, and S be the area of the rhombus.
The area of triangle ABD is:
S/2 = (1/2)AB*AD sin(40)
S/2 = AD^2 sin(40) / 2 .........(1)

From triangle APD:
AD cos(20) = 10
AD = 10 / cos(20)

Substitute for AD in (1):
S/2 = 100 sin(40) / 2cos^2(20)
S = 100 sin(40) / cos^2(20)
S = 72.79.

2007-08-09 10:25:23 · answer #2 · answered by Anonymous · 0 1

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