how do i find the area of square if the given is its diagonal?

Answer 1

You probably need to use Pythagoras, unless there's an easy way I'm missing...

By Pythagoras, a^2 + b^2 = c^2 (The sum of the squares of the shortest sides is equal to the square of the longest side.)

As it's a square, a and b are equal, so 2(a^2) = c^2.

a^2 = (c^2)/2

so a = square root of (c^2/2)

That gives you the length of the sides, so square to get the area, which takes you back to (c^2/2)

If I didn't make it clear enough earlier, c is the length of the diagonal, so area = (diagonal squared)/2

Answer 2

If it's a square, diagonals bisect at right angles. So if you have a diagonal, it separates the square into two triangles of base equal to diagonal, and height half that length. The area of one such triangle is equal to (1/2diagonal) squared or diagonal squared divided by 4. Two such triangles (ie. the square) would then be
(diagonal^2)/2.

Of course...pythagoras' theorem also works...

Answer 3

Square means the two sides are equal. Diagonal = Side / sin 45 or side = Diagonal X sin 45

Area = Side X Side = Diagonal ^2 X (sin 45)^2
= Diagonal ^2 X 0.724

Answer 4

Hi
Area of a square can be obtaind if you know the value of one of the sides.If you are given the diagonal,then you have to find the side by using Pythagoras theorem.Sum of the square of the sides =square of the hypotenuseBut the sides here are equal.So suare the diagonal.That is equal to the sum of the squares of your sides.Then divide the square of the diagnol by 2 and then take square root.That is the side.Square that value to give the area.

Answer 5

Diagonal of a square = sq.root 2 x length of side (a).

So using the diagonal's length, find a.

You get area using the formula Area = a^2

Answer 6

relationship between diagonal and side is
D=(root 2).A
=>A=D/(root 2)
A =side of square D=diagonal of square
aim is to find area of square= A*2=(D/(root2))*2=(D*2)/2
( A*2)+(A*2)=D*2 since diagonal &two sides of squre form a rectangle
=>2A*2=D*2 =>A=D/(root 2)

Answer 7

providing A is the side of the square, D - its diagonal, S - the area, C=45degrees=the angle between the diagonal and the side:

A=D*cosC
S=A^2
S=(D*cosC)^2
S=2*D^2
because (cos45degrees)=2

Answer 8

Area = a
Length of side = s
Diagonal = d

Using pythagoras

d² = s² + s²
d² = 2s²

a = s²

d² = 2a

d²/2 = a

Area is d²/2 units²