Find the area of a square of whose diagonal is 8cm
The diagonal of a square divides it into two congruent right triangles. Let's denote the length of each side of the square as s.
According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the other two sides.
So, we can write the following equation:
s^2 + s^2 = 8^2
Simplifying the equation, we get:
2s^2 = 64
Dividing by 2, we have:
s^2 = 32
Taking the square root of both sides, we find:
s ≈ √32 ≈ 5.657
Therefore, the length of each side of the square is approximately 5.657 cm.
To find the area of the square, we can square the length of one side:
Area = s^2 = (5.657)^2 ≈ 32 cm^2
Thus, the area of the square with a diagonal of 8 cm is approximately 32 square centimeters.
To find the area of a square given its diagonal, you can use the Pythagorean theorem.
Let's say the length of one side of the square is "s" cm.
According to the Pythagorean theorem, we have:
diagonal^2 = side^2 + side^2
8^2 = s^2 + s^2
64 = 2s^2
Divide both sides by 2:
32 = s^2
Take the square root of both sides:
√32 = s
s ≈ 5.66 cm (rounded to two decimal places)
Now that we know the length of one side is approximately 5.66 cm, we can find the area of the square:
Area = side^2
Area = (5.66)^2
Area ≈ 32 cm^2 (rounded to two decimal places)
Therefore, the area of the square with a diagonal of 8 cm is approximately 32 cm^2.