The diagonal multiplied by sin(angle) gives one side of the rectangle and the diagonal times cos(theta) gives the other. So the area is (diagonal)2 x cos(theta) x sin(theta).
You need to know more...either the angle or the length of one of the sides.
If the only known fact is the length of the diagonal then the width and length of the rectangle CANNOT be determined. The diagonal could be that of a square, or of a rectangle that is very long but quite narrow. Consequently at least one more fact is required such as; the dimension of either the length or the width, or the angle that the diagonal makes to the base of the rectangle or even the area of the rectangle.
The one alternative to find the area of a rectangle is when you are given the length of one diagonal and its slope.
Divide the rectangle in two triangles and then use the pythagorean theorem to find the remaining sides.
First divide the perimeter by 2 then subtract the diagonal from this. The number left with must equal two numbers that when squared and added together equals the diagonal when squared (Pythagoras' theorem) These numbers will then be the length and height of the rectangle.
You need to know more...either the angle or the length of one of the sides.
You need to use trigonometry cosine (angle) = length/diagonal diagonal = length/cos(angle)
if a rectangle has width of 5 and diagonal with lenght of 13, what is the area of the rectangle? Use Pythagoras' theorem to find the length of the rectangle which will be 12 5*12 = 60 square units
If the only known fact is the length of the diagonal then the width and length of the rectangle CANNOT be determined. The diagonal could be that of a square, or of a rectangle that is very long but quite narrow. Consequently at least one more fact is required such as; the dimension of either the length or the width, or the angle that the diagonal makes to the base of the rectangle or even the area of the rectangle.
To find the diagonal length of a rectangle use Pythagoras' theorem for a right angle triangle.
The one alternative to find the area of a rectangle is when you are given the length of one diagonal and its slope.
Divide the rectangle in two triangles and then use the pythagorean theorem to find the remaining sides.
240 sq m
You can't. Suppose for instance your rectangle is 1xA, then the diagonal length is sqrt(1+A**2). But if your rectangle is sqrt(A)xsqrt(A) then your diagonal length is sqrt(2*A). The only thing one can say for sure is that the diagonal length is at least sqrt(2*A).
First divide the perimeter by 2 then subtract the diagonal from this. The number left with must equal two numbers that when squared and added together equals the diagonal when squared (Pythagoras' theorem) These numbers will then be the length and height of the rectangle.
By using the trigonometric ratios of Sine and Cosine. The diagonal forms the hypotenuse of a right angled triangle with the length and width of the rectangle forming the other two sides of the triangle - the adjacent and opposite sides to the angle. Then: sine = opposite/hypotenuse → opposite = hypotenuse x sine(angle) cosine = adjacent/hypotenuse → adjacent = hypotenuse x cosine(angle)
Doesn't describe the problem well enough.