What is the area of a rhombus with a 45 degree angle and sides of 10ft.?
10 * 10sin45
To find the area of a rhombus, you can use the formula: Area = (diagonal1 * diagonal2) / 2.
In this case, since we only have the measure of one angle and the side length, we need to find the lengths of the diagonals.
In a rhombus, the diagonals are perpendicular bisectors of each other, and they split the rhombus into four congruent right triangles. Since the given angle is 45 degrees, each of these triangles is a 45-45-90 triangle.
In a 45-45-90 triangle, the sides are in the ratio 1:1:√2. This means that the length of the hypotenuse (which is half of the diagonal) is √2 times the length of each leg (which is the side length of the rhombus).
Given that the side length is 10ft, we can calculate the length of the diagonal (2 times the hypotenuse) using the Pythagorean theorem:
Leg = 10ft
Hypotenuse = Leg * √2 = 10ft * √2 = 10√2 ft
Diagonal = 2 * Hypotenuse = 2 * 10√2 ft = 20√2 ft
Now that we have the lengths of the diagonals, we can calculate the area of the rhombus using the formula:
Area = (diagonal1 * diagonal2) / 2
Area = (20√2 ft * 20√2 ft) / 2
Area = (400 ft² * 2) / 2
Area = 400 ft²
Therefore, the area of the rhombus with a 45-degree angle and sides of 10ft is 400 square feet.