The diagonals of a square each measure 7 feet. How do you find the area of the square?

2 Answers
Oct 19, 2015

Answer:

4.95 feet

Explanation:

You must use trigonometry.
Since it is a square, and each angle in a square is 90 degrees, the two angles of the triangle the diagonal makes is half of that, 45.

#sintheta = #(opposite)/hypoteneus
#sin45 = o/7#
#7sin45= o#
#o = 4.94974746831#

Answer:

You can use the Pythagorean Theorem

#A=24.5# square feet

Explanation:

The Pythagorean Theorem says that in a square triangle the square of the hypotenuse (a) is equal to the square of one leg (b) plus the square of the other lag (c):

#a^2=b^2+c^2#

The diagonal of a square form a square triangle with two of the sides (see figure below) and (b) is equal to (c). Therefore, the equation can be written as below:

#a^2=b^2+b^2#

#7^2=b^2+b^2#

#49=2b^2#

#b^2=49/2#

#b=sqrt(49/2)# feet (side of the square)

The area is the product of two sides

#A=sqrt(49/2)xxsqrt(49/2)=49/2=24.5# square feet
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