Question

Two rhombuses have sides with lengths of `1`. If one rhombus has a corner with an angle of `(7pi)/12` and the other has a corner with an angle of `(3pi)/4`, what is the difference between the areas of the rhombuses?

Answer 1

Difference between areas of A & B = 0.4482#

Explanation:

Let the two rhombuses be A & B.

Let’s consider rhombus A with angle `(7pi)/12` & side = 1
Height `h1 = 1 * sin (pi/12) = 0.2588`
Area of Rhombus A = 1 * 0.2588 = 0.2588#

Let’s consider rhombus B with angle `(3pi/4)` & side = 1
Height `h2 = 1 * sin (pi/4) = 1/sqrt2 = 0.707`
Area of Rhombus B= 1 * 0.707 = 0.707#

Difference between areas of A & B `= 0.707 - 0.2588 = 0.4482`