what is the area of a rhombus with a 60 degree angle and sides 5 cm long? (round to the nearest 10th)

b = 5cm.

h = 5sin60 = 4.33cm.

A = bh = 5 * 4.33 = 21.7cm^2.

To find the area of a rhombus, you can use the following formula:

Area = (d₁ * d₂) / 2

where d₁ and d₂ are the lengths of the diagonals of the rhombus.

To calculate the diagonals of the rhombus, you can use the fact that the diagonals of a rhombus are perpendicular bisectors to each other and divide the rhombus into four congruent right-angled triangles.

Given that one angle of the rhombus is 60 degrees and each side is 5 cm long, we can use trigonometric ratios to calculate the lengths of the diagonals.

In a right-angled triangle, the opposite side length (abbreviated as "opp") is equal to the side length multiplied by the sine of the angle. Therefore, in our case, the length of the opposite side ("opp") is equal to 5 cm multiplied by the sine of 60 degrees.

opp = 5 cm * sin(60°)

opp = 5 cm * √3 / 2

opp ≈ 8.7 cm (rounded to the nearest tenth)

Since the diagonals of a rhombus bisect each other at right angles, the length of each diagonal will be twice the length of the opposite side.

diagonal = 2 * opp

diagonal = 2 * 8.7 cm

diagonal ≈ 17.4 cm (rounded to the nearest tenth)

Now that we have the lengths of the diagonals, we can substitute them into the area formula to find the area of the rhombus.

Area = (17.4 cm * 8.7 cm) / 2

Area ≈ 75.6 cm² (rounded to the nearest tenth)

Therefore, the area of the rhombus with a 60-degree angle and sides 5 cm long is approximately 75.6 cm².