SOLUTION: What is the area of a square with diagonals 10cm long

Question 284017: What is the area of a square with diagonals 10cm long
Found 2 solutions by checkley77, solver91311:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
a^2+a^2=10^2
2a^2=100
a^2=100/2
a^2=50
a=sqrt50
a=7.07 cm is the length of the sides of the square.
7.07^2=50 cm^2
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If the diagonal of a square is 10 cm, then you can either remember that the sides of an isosceles right triangle are in proportion , multiply times 10 to get as the measure of the side of the square. Which value you can then multiply by itself to obtain the desired area, or...

use Pythagoras to say:

Then solve for which is the area of the square, or...

You could use Pythagoras to say:

for ANY square of side and diagonal and then write:

Which is a formula for the area of any square given the measure of the diagonal.

John

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