Question

Two rhombuses have sides with lengths of `7`. If one rhombus has a corner with an angle of `pi/3` and the other has a corner with an angle of `(5pi)/8`, what is the difference between the areas of the rhombuses?

Answer 1

`|A_(R_1) - A_(R_2)| ~~2.83`

Explanation:

Given : Two Rhombuses, `R_1 (7, pi/3); R_1 (7, (5pi)/8)`
Required : The difference in area of `A_(R_1) - A_(R_2)`
Solution strategy use the area formula for a parallelogram with sides - `s_1 and s_2` with an angle `theta` in between them;
`A_diamond = |s_1|*|s_2|*sintheta`
`A_(R_1) = |7|*|7|*sin(pi/3)~~ 42.43`
`A_(R_1) = |7|*|7|*sin(5/8pi)~~45.27`
`|A_(R_1) - A_(R_2)| ~~2.83`