## http://prntscr.com/ix3zya This image shows a square pyramid. What is the surface area of this square pyramid? 36 ft² 72 ft² 78 ft² 84 ft²

Mar 27, 2018

36 $f {t}^{2}$

#### Explanation:

surface area is lateral
a perpendicular line from the top angle to the bottom is a perpendicular bisector so the line is now 3 and 3
so in triangle one (as i named it) we have a isosceles triangle (45-45-90) or a special right triangle (x-x-xsqrt2).
the area of triangle one is $\frac{1}{2} \cdot b h$ , so $\frac{1}{2} \cdot 3 \cdot 3$, i.e. $\frac{9}{2}$
$\frac{9}{2}$area of one triangle, as the base is a square all the measures are same so the area of all triangles will be same. on each side we have 2 triangles and we have 4 side so 8 triangles.
the total suface area is $\left(\frac{9}{2} \cdot 8\right) = 36$