A pyramid has a square bottom, with an area equal to 64 squares meters. the height of the pyramid is 7 inches. if you start at the top of the pyramid and slide all the way down the middle of one of the sides how many feet will you move?
Draw a diagram of a vertical cross-section parallel to one side of the base.
8^2 + 7^2 = d^2
where d is the length down the middle of the face.
To solve this problem, we need to find the slant height of the pyramid by using the Pythagorean theorem.
Let's begin by finding the length of one side of the square base. The area of the square base is given as 64 square meters. Since the base is square, we can find the length of one side by taking the square root of the area.
√64 = 8 meters
Next, we need to convert the height of the pyramid from inches to meters. Since 1 inch is equal to 0.0254 meters, the height of the pyramid is:
7 inches * 0.0254 meters/inch = 0.1778 meters
Now, we can use the Pythagorean theorem to find the slant height of the pyramid. The slant height is the hypotenuse of a right triangle formed by the height and half of the base.
Using the formula, a^2 + b^2 = c^2, where a is half the base length (4 meters), b is the height (0.1778 meters), and c is the slant height, we can solve for c.
4^2 + 0.1778^2 = c^2
16 + 0.03164164 = c^2
16.03164164 = c^2
c ≈ √16.03 ≈ 4.003 meters
Finally, since the length of the slant height is given in meters, we need to convert it to feet. Since 1 meter is equal to 3.28084 feet, the length of the slant height in feet is:
4.003 meters * 3.28084 feet/meter ≈ 13.12 feet
Therefore, if you slide all the way down the middle of one side of the pyramid, you would move approximately 13.12 feet.
To find the answer, we need to calculate the slant height of the pyramid first. With the height given as 7 inches, we have a right triangle formed by the slant height (hypotenuse), the height, and half of the base (half of the length of one side of the square bottom).
Using the Pythagorean theorem, we can solve for the slant height (l):
l² = (7/2)² + 7²
l² = 24.5 + 49
l² = 73.5
l ≈ 8.575 meters (rounded to three decimal places)
Now we know the slant height of the pyramid. To determine the distance you move when sliding down the middle of one of the sides, we need to calculate the length of that side.
Since the bottom of the pyramid is a square with an area of 64 square meters, each side of the square has an area of √64 = 8 meters.
Now, when sliding down the middle of one of the sides, you are essentially moving along the slant height. Thus, the distance you move is equal to the slant height, which is approximately 8.575 meters.
To convert this to feet, we know that 1 meter is approximately equal to 3.281 feet. Multiplying the distance in meters by the conversion factor, we get:
8.575 meters * 3.281 feet/meter ≈ 28.132 feet (rounded to three decimal places)
Therefore, when you slide all the way down the middle of one of the sides of the pyramid, you will move approximately 28.132 feet.