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

2 Answers
Oct 19, 2015

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

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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