Find the area of a rhombus with a 45 degree angle and sides of 12m long?

area = (12)(12)sin 45° = 144(√2/2)

= 72√2= appr 101.8

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

Area = (diagonal 1 * diagonal 2) / 2

Since the problem provides the lengths of the sides, we can determine the lengths of the diagonals using the properties of a rhombus.

In a rhombus, the diagonals are perpendicular bisectors of each other. This means that they divide the rhombus into four congruent right triangles.

Given that the angles in a rhombus are equal, we can determine that each angle in this rhombus is 45 degrees.

Since the diagonals bisect the 45-degree angles, each right triangle in the rhombus is a 45-45-90 triangle, where the hypotenuse is given as the length of the rhombus side (12 m).

Using the properties of a 45-45-90 triangle, we can determine that the length of each diagonal is:

diagonal = side length * √2
diagonal = 12 m * (√2)

Substituting in the values, we get:

diagonal = 12 m * (1.414)
diagonal = 16.972 m (approx)

Now that we have the lengths of the diagonals, we can find the area of the rhombus:

Area = (diagonal 1 * diagonal 2) / 2
Area = (16.972 m * 16.972 m) / 2
Area = 288.021 m² (approx)

Therefore, the area of the rhombus is approximately 288.021 square meters.

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

Area = (diagonal1 * diagonal2) / 2

However, since you have been given the side length, we need to find the diagonals first.

In a rhombus, opposite angles are congruent, so if one angle is 45 degrees, the opposite angle is also 45 degrees.

To find the diagonals, we can use the properties of a rhombus. In a rhombus, the diagonals bisect the opposite angles.

Since we have a 45 degree angle, which is bisected by the diagonal, we can form a right-angled triangle.

In this right-angled triangle, the hypotenuse is the side of the rhombus (12m), and the opposite angle is 45 degrees.

Now, we can use the trigonometric function sine to find the length of the diagonal.

sin(45 degrees) = opposite / hypotenuse
sin(45 degrees) = x / 12m

Using the sine of 45 degrees (which is √2 / 2), we can solve for x:

(√2 / 2) = x / 12m
x = (√2 / 2) * 12m
x = 6√2 m

Now that we have the length of one diagonal, we know that the other diagonal will also have the same length since the diagonals of a rhombus are equal.

So, the length of both diagonals is 6√2 m.

Now we can calculate the area of the rhombus:

Area = (diagonal1 * diagonal2) / 2
Area = (6√2 m) * (6√2 m) / 2
Area = (36 * 2) m^2 / 2
Area = 72 m^2

Therefore, the area of the rhombus with a 45-degree angle and sides of 12m long is 72 square meters.