Calculate the side of the square base.if the diagonal of the base of a square prism is 8,49 cm and the height is 12 cm
draw the figure. If the diagonol of the prism is 8.49, then the diagonal of the base is 8.49/sqrt2.
If the diagonal of the base is 8.49/sqrt2, then the side of the base is
(8.49/sqrt2)*1/sqrt2=8.49/2
To calculate the side of the square base of the prism, you can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the diagonal of the square base is given as 8.49 cm, and the height of the prism is given as 12 cm.
Let's assume that each side of the square base is 's' cm.
Using the Pythagorean theorem, we can write the equation as:
s^2 + s^2 = (8.49)^2
Simplifying the equation, we get:
2s^2 = (8.49)^2
Divide both sides of the equation by 2:
s^2 = (8.49)^2 / 2
Take the square root of both sides:
s = √((8.49)^2 / 2)
Using a calculator, we can find the square root of (8.49^2 / 2) to get the value of 's'.
s ≈ √(72.0201 / 2)
s ≈ √36.01005
s ≈ 6 cm
Therefore, the side of the square base of the prism is approximately 6 centimeters.