Question

DUE IN 30MIN
Pyramid
The height of the pyramid is 481 feet. If the lateral side is 652 feet,
what is the TOTAL length of the bottom of the pyramid face?

Answer 1

Answer:

880.3 ft

Step-by-step explanation:

To find the total length of the bottom of the pyramid face, we can use the Pythagorean theorem in combination with the given height and lateral side length.

Let's denote:

• $h$ as the height of the pyramid (481 feet).
• $s$ as the lateral side length (652 feet).
• $l$ as the total length of the bottom of the pyramid face that we want to find.

Using the Pythagorean theorem, the length of the lateral side $s$ can be related to the height $h$ and the half of the total length of the bottom of the pyramid face $l/2$:

$s^2 = \left(\dfrac{l}{2}\right)^2 + h^2$

We need to solve for $l$. First, we rearrange the equation:

$\left(\dfrac{l}{2}\right)^2 = s^2 - h^2$

$\left(\dfrac{l}{2}\right)^2 = (652\, \textsf{ft})^2 - (481\, \textsf{ft})^2$

Now, we calculate:

$\left(\dfrac{l}{2}\right)^2 = (425104\, \textsf{ft}^2) - (231361\, \textsf{ft}^2)$

$\left(\dfrac{l}{2}\right)^2 = 193743 \, \textsf{ft}^2$

$\dfrac{l^2}{4} = 193343\, \textsf{ft}^2$

Now, we solve for $l$:

$l^2 = 4 \times 193343\, \text{ft}^2$

$l^2 = 774972\, \textsf{ft}^2$

$l = \sqrt{774972\, \textsf{ft}^2}$

$l \approx 880.32494 \, \textsf{ft}$

$l \approx 880.3 \, \textsf{ft (in 1 d.p.)}$

Thus, the total length of the bottom of the pyramid face is approximately $880.3$ feet.