what is the diagonal of a square is 14 m, what is the area?
Please clarify your question.
Currently, it is asking what the diagonal is, but also stating that the diagonal is 14 m.
surely you meant
If the diagonal of a square is 14 m, what is the area?
well, if the diagonal is d, the area is d^2/2
because if the square's side is s, the area is s^2. The diagonal is s√2, so d^2 = 2s^2
To find the area of a square when only the length of its diagonal is known, we need to use the Pythagorean theorem.
In a square, the diagonal divides the square into two congruent right triangles. According to the Pythagorean theorem, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
Let's denote the length of each side of the square as "s". The diagonal of a square forms two right triangles, each with a hypotenuse equal to the length of the diagonal.
Using the Pythagorean theorem, we have:
s^2 + s^2 = (14m)^2
Simplifying the equation, we get:
2s^2 = 196m^2
Divide both sides of the equation by 2:
s^2 = 98m^2
To find the area of the square, we need to square the length of one side since all sides of the square have the same length:
Area = s^2 = (98m^2)
Therefore, the area of the square is 98 square meters.