# Two rhombuses have sides with lengths of #9 #. If one rhombus has a corner with an angle of #pi/6 # and the other has a corner with an angle of #(pi)/4 #, what is the difference between the areas of the rhombuses?

≈ 16.79 square units

A rhombus has 4 equal sides and is constructed from 2 congruent isosceles triangles.

Now the area of 2 congruent triangles ( area of rhombus) is

so difference in area = 57.29 - 40.5 = 16.79 square units

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

To find the area of a rhombus, you can use the formula: ( A = \frac{d_1 \times d_2}{2} ), where ( d_1 ) and ( d_2 ) are the lengths of the diagonals.

For a rhombus with side length ( s ) and an angle ( \theta ) between two adjacent sides, the diagonals can be found using the formula: ( d_1 = s \times \sqrt{2 + 2\cos(\theta)} ) and ( d_2 = s \times \sqrt{2 - 2\cos(\theta)} ).

Using these formulas, you can calculate the areas of the two rhombuses and then find their difference.

For the rhombus with an angle of ( \frac{\pi}{6} ), the diagonals are ( d_1 = 9\sqrt{3} ) and ( d_2 = 9 ). The area is ( A_1 = \frac{9\sqrt{3} \times 9}{2} = \frac{81\sqrt{3}}{2} ).

For the rhombus with an angle of ( \frac{\pi}{4} ), the diagonals are ( d_1 = 9\sqrt{2} ) and ( d_2 = 9\sqrt{2} ). The area is ( A_2 = \frac{9\sqrt{2} \times 9\sqrt{2}}{2} = \frac{81 \times 2}{2} = 81 ).

The difference between the areas is ( A_1 - A_2 = \frac{81\sqrt{3}}{2} - 81 ).

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

- A quadrilateral has sides of lengths 3cm,4cm,5cm and 'x' cm. What is the greatest possible integral value of 'x'?
- A parallelogram has sides with lengths of #15 # and #8 #. If the parallelogram's area is #8 #, what is the length of its longest diagonal?
- The coordinates of the vertices of a parallelogram ABCD are A(0,0) B(b,y), C(a+b,y) and D(a,0). If ABCD is a rhombus, how would you express y in terms of a and b?
- Given A(1, 1), B(0,5), C(4,4), and D(5, 0). Use the fact that if the diagonals of a parallelogram are perpendicular, then it is a rhombus to prove ABCD is a rhombus?
- A parallelogram has sides with lengths of #16 # and #9 #. If the parallelogram's area is #96 #, what is the length of its longest diagonal?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7