Question

Two rhombuses have sides with lengths of `3`. If one rhombus has a corner with an angle of `pi/2` and the other has a corner with an angle of `(3pi)/8`, what is the difference between the areas of the rhombuses?

Answer 1

Difference between the areas of 2 rhombus is

`A_d = A_1 - A_2 = 9 - 8.31 = 0.69` sq units

Explanation:

Area of rhombus `A = a^2 sin theta`

Given : `a_1 = a_2 = 3, theta_1 = pi/2, theta_2 = (3pi)/8`

Area of Rhombus `A_1 = (a_1)^2 sin theta_1`

`A_1 = 3^2 sin (pi/2) = 9` sq units, it’s a square since `theta = 90^@ = (pi/2)^c`

Area of Rhombus `A_2 = (a_2)^2 sin theta_2`

`A_2 = 3^2 sin ((3pi)/8) = 8.31` sq units

Difference between the areas of 2 rhombus is

`A_d = A_1 - A_2 = 9 - 8.31 = 0.69` sq units