The diagonal of a rectangle is 25 meters long makes an angle of 36 ° with one of the rectangle. Find the area and the perimeter of the parallelogram.

how to find the b to arrive to the area?

Please proof-read your work.

L = 25*Cos36 =
W = 25*sin36 =

Ar = L*W. = Area of rectangle.
Pr = 2L + 2W.

At = 0.5L*W = Area of triangle.
Pt = L+W+25.

To find the area of a parallelogram, we need to know both the base and the height. In this case, the diagonal of the rectangle can be used as the base of the parallelogram.

To find the height (h) of the parallelogram, we can use trigonometry. Since the diagonal of the rectangle makes an angle of 36° with one of the sides of the rectangle, we can find the height using the sine function.

1. Identify the angle of interest: In this case, the angle is 36°.

2. Set up the trigonometric equation: We have sin(36°) = opposite/hypotenuse = h/25.

3. Solve for the height (h): Rearrange the equation to solve for h. Multiply both sides of the equation by 25, then take the sin^-1 (inverse sine) of both sides. This gives us h = 25 * sin(36°).

Now that we have the height (h), we can calculate the area and perimeter of the parallelogram.

Area of a parallelogram: A = base * height

Perimeter of a parallelogram: P = 2 * (length + width)

Since the opposite sides of a parallelogram are equal in length, we can set the base of the parallelogram as the length of the rectangle.

To find the width (w) of the parallelogram, we can use the Pythagorean theorem. The width of the rectangle is the hypotenuse of a right triangle formed by the rectangle and the height.

1. Set up the Pythagorean theorem equation: w^2 + h^2 = diagonal^2

2. Substitute the known values: w^2 + (25 * sin(36°))^2 = 25^2

3. Solve for w: Rearrange the equation to isolate w, by subtracting (25 * sin(36°))^2 from both sides of the equation. Then, take the square root of both sides to find the value of w.

Now that we have the base and height of the parallelogram, we can calculate the area and perimeter using the formulas mentioned earlier.