Two rhombuses have sides with lengths of #5 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(11pi)/12 #, what is the difference between the areas of the rhombuses?

Answer 1

Difference in areas is #color(red)(0)#

Area of rhombus #= (1/2) * d_1 * d_2 or a * h# Where #d_1 , d_2 # are the diagonals, a is the side and h is the altitude.

In this case we will use the formula Area = a * h.

Rhombus 1 #h = a sin theta = 5 * sin (pi/12) = 1.2941# Area = a * h = 5 * 1.2941 = 6.4705#

Rhombus 2 #h a sin theta = 5 * sin (11pi)/12 = 1.2941# Area = a * h = 5 * 1.2941 = 6.4705#

Both the rhombus will have same area as #sin (pi/12) = sin ((11pi)/12)# Hence the difference in areas is 0

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Jayden Jackson

The difference between the areas of the two rhombuses is 25.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.