A sign is in the shape of a rhombus with a 60° angle and sides of 2 cm long. Find the area of the sign to the nearest tenth.

About 1.2 cm squard

To find the area of the sign, we can use the formula:

Area = (d1 * d2) / 2

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

Since the rhombus has a 60° angle, it is an equilateral rhombus, which means all sides and diagonals are equal.

Given that the sides of the rhombus are 2 cm long, each diagonal is also 2 cm.

Now, substitute the values into the formula:

Area = (2 * 2) / 2
= 4 / 2
= 2 cm²

So, the area of the sign is 2 square centimeters.

To find the area of the sign, we can use the formula for the area of a rhombus:

Area = (diagonal1 * diagonal2) / 2

In this case, since we are not given the length of the diagonals, we need to find them first.

To find the length of the diagonals, we can use the properties of a rhombus. A rhombus has two pairs of opposite congruent angles, and the diagonals of a rhombus bisect these angles.

Since one of the given angles is 60°, the opposite angle is also 60°. The other two angles are supplementary to the given angles and are also congruent. So, each of the other two angles is (180° - 60°) / 2 = 60°.

Now we can use the law of cosines to find the lengths of the diagonals. Let's label the sides of the rhombus as a, b, and c.

In a rhombus, a² = b² + c² - 2bc*cos(A), where A is the angle opposite side a.

In this case, since the sides of the rhombus are 2 cm long, we have:

2² = b² + c² - 2bc*cos(60°)

Simplifying this equation, we get:

4 = b² + c² - bc

Since the sides of the rhombus are congruent, b = c, so we can rewrite the equation as:

4 = b² + b² - b²

Simplifying further, we have:

4 = 2b²

Dividing both sides by 2, we get:

2 = b²

Taking the square root of both sides, we get:

b = √2

Therefore, the length of each diagonal is √2 cm.

Now we can substitute the values of the diagonals into the formula for the area of a rhombus:

Area = (diagonal1 * diagonal2) / 2

Area = (√2 * √2) / 2

Area = 2 / 2

Area = 1 square cm

So, the area of the sign is 1 square cm to the nearest tenth.

Area = (2)(2)sin60°

= .....