help plz

The sum of the areas of all 8 triangles is the lateral area.

And, each of these triangles are the same size.

So...

lateral area = 8 * area of one of these triangles

lateral area = 8 * (1/2) * base * height

From the Pythagorean theorem:

6² + 6² = height²          $\rightarrow \quad \text{height} = \sqrt{72}=6\sqrt2$

lateral area = 8 * (1/2) * 5 * 6√2

lateral area = 120√2     ≈     169.7   cm²

The lateral  area will be comprised of 8 congruent triangles

The slant height  of each triangle  = sqrt (6^2 + 6^2)  = sqrt (72)  = 6sqrt (2) cm

And the base of each triangle  = 5 cm

So.....the total lateral  area  =

8 * (1/2) (base) (slant height)  =

8 (1/2) (5) (6sqrt(2) ) ≈  169.7 cm ^2