turkey-yks 2023 Q29

turkey-yks · Other · yks-ayt Trig Proofs Trigonometric Equation Constraint Deduction
In Figure 1, a parallelogram with two sides of lengths 4 units and 8 units and the angle between these sides measuring $x$ degrees is given. In Figure 2, a parallelogram with two sides of lengths 4 units and 6 units and the angle between these sides measuring $2x$ degrees is given.
If the area of the parallelogram in Figure 1 is 24 square units, what is the area of the parallelogram in Figure 2 in square units?
A) $6\sqrt{7}$ B) $7\sqrt{7}$ C) $8\sqrt{7}$ D) $9\sqrt{7}$ E) $10\sqrt{7}$
In Figure 1, a parallelogram with two sides of lengths 4 units and 8 units and the angle between these sides measuring $x$ degrees is given. In Figure 2, a parallelogram with two sides of lengths 4 units and 6 units and the angle between these sides measuring $2x$ degrees is given.

If the area of the parallelogram in Figure 1 is 24 square units, what is the area of the parallelogram in Figure 2 in square units?

A) $6\sqrt{7}$
B) $7\sqrt{7}$
C) $8\sqrt{7}$
D) $9\sqrt{7}$
E) $10\sqrt{7}$