A regular square pyramid has a height of 2 and lateral edges of length 10. Find lateral area A regular square pyramid has a height of 2 and lateral edges of length 10. What is the lateral area?

First, we will find half of the diagonal of the square using the Pythagorean Theorem.

Let $d$ be half the diagonal of the square.

$2^2 + d^2 = 10^2$

$4+d^2 = 100$

$2d = 2\sqrt{96}$ = 18.547236991

Using the formulas:

$A=a^2$

$d=2a$

Assuming if A = area, the area of the base square would be:

$A=\frac12 d^2$

$A=\frac12 \times 18.55^2$ (diagonal)

$A≈172$

The side length of the base will be $\sqrt{172} ≈ 13.11$

Finally, we will find the Lateral Surface Area, L, using the formula:

L= $a \sqrt {a^2+4h^2}$

L= $13.11\times\sqrt{13.11^2+4\times2^2}≈179.69411$

The lateral surface area of the square based pyramid is $≈179.7$