Question

use the diagram of a square pyramid to answer the question. what is the length of the slant height, l? a. 3 in. b. 9 in. c. $sqrt{39}$ in. d. $sqrt{41}$ in. e. $sqrt{89}$ in.

Explanation:

Step1: Identify right - triangle components

We can consider a right - triangle within the square pyramid. The height of the pyramid is 5 in and half of the base side length is $\frac{8}{2}=4$ in. The slant height $L$ is the hypotenuse of this right - triangle.

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $a = 4$ in, $b = 5$ in and $c = L$. So $L=\sqrt{4^{2}+5^{2}}$.

Step3: Calculate the value of $L$

$L=\sqrt{16 + 25}=\sqrt{41}$ in.

Answer:

D. $\sqrt{41}$ in.