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Using Pythagoras' theorem which says that the square on the hypotenuse (in this case the diagonal) is equal to the sum of the squares on the other two sides (which in the case of a square would be equal in length).
so if the diagonal measured 10 units, the square on the diagonal would be 100 square units. And as this = 2*the squares on the other sides, the square on one side would be 100/2 = 50 square units.
As a square has sides of equal length the square on one side is actually the area of the square.
i.e. the area of a square with a diagonal of 10 units is 50 square units.
or generically the area of a square with a diagonal of length 'x' = (x2)/2
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How do you find the side of a square if you know its diagonal?
Divide the length of the diagonal of a square by 1.4142 (which is the square root of 2) to find the length of a side. Similarly, to find the length of the diagonal of a square, multiply the length of a side by 1.4142.
How do you find the area of a rectangle with the diagonal of 13 and a width of 5?
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
What is the length of the diagonal of a square with an area of 64?
To find the length of the diagonal of a square with an area of 64 square units, we first need to calculate the side length of the square. Since the area of a square is side length squared (A = s^2), we can find the side length by taking the square root of the area (s = √A). In this case, the side length of the square is 8 units. To find the length of the diagonal, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides (a^2 + b^2 = c^2). Since a square can be divided into two right triangles with the diagonal as the hypotenuse, we can calculate the diagonal length using d = √(s^2 + s^2), where d is the diagonal length and s is the side length. Substituting the side length of 8 units into the formula, we get d = √(8^2 + 8^2) = √(64 + 64) = √128 = 8√2 units. Therefore, the length of the diagonal of a square with an area of 64 square units is 8√2 units.
Find the area of a square with a diagonal of 6 yds?
You can use trigonometry to find the solution. A diagonal divides a square into two triangles, known as "45-45-90" triangles (because of the measures of each angle). According to a law of the same name, the hypotenuse (side opposite of the 90o angle) has a length equal to the length of a leg (side opposite of a 45o angle) times the square root of two. So, since the hypotenuse is a diagonal, you will find that the length of each side of the square is 6 divided by the square root of 2. Find the square of this, and you have the total area: 18 square yards.
How do you find the area of a square with a diagonal of 10?
If the diagonal is 10 we know all sides are equal so from pythagoraen theorem each side is 7.07 inch length Area = 7.07 x 7.07 = 50
How do you find the area of a square given only the length of its diagonal?
Given the length of the diagonal of the square ... call it 'D units'. The area of the square is (1/2 D2) (same units)2.
How do you find the length of each side of a square?
If you are given the area of the square, then the length of each side is the square root of the area. If you are given the length of the diagonal of a square, then the lenght of each side is equal to the length of the diagonal divided by the square root of 2. l=sqrt(a) l=d/[sqrt(2)] l=length of side, d=diagonal, a=area, sqrt means square root
Square area equals 8 hectare find diagonal in km?
The square has a diagonal measurement of: 1.13 km
What is the area of a square with a diagonal of 14?
To find the area of a square with a diagonal of 14, we first need to determine the length of one side of the square. Using the Pythagorean theorem, we can calculate that the side length is 7√2. Then, we can find the area of the square by squaring the side length, which gives us 98 square units.
How do you find the area of a square whose diagonal is 7.5 cm?
Check
Find the area of a square with a diagonal of 8cm?
32 cm² = 8cm²/2
How do you find the area of a parallelogram if only the diagonal is given?
You cannot. There is not enough information.
What is the formula to find one side of a square?
The answer will depend on what information about the square you have: its perimeter, area, length of diagonal.
How do you find the edge of a cube if the measure of the diagonal is given?
The longest diagonal in a cube is equal to the length of the edge, multiplied by the square root of 3.
How do you find the side of a square if you know its diagonal?
Divide the length of the diagonal of a square by 1.4142 (which is the square root of 2) to find the length of a side. Similarly, to find the length of the diagonal of a square, multiply the length of a side by 1.4142.
How do you calculate the diagonal of the square?
You multiply the length of a side by the square root of 2.If you only have the area, square root it to find the length of a side.
How do you find the volume of a cubical box when diagonal is given?
Cool question ! Answer - half it then cube it to prove it - an example for you if cube diagonal (not square diagonal) is 100, then using pythagoras theorm the square diagonal = 70.71068, If square the square diagonal = 70.71068, then using pythagoras theorm the side length = 50 therefore the volume = 50 ^ 3 = 25000 units works with any numbers
