Question

a square pyramid is given. what is the surface area of the pyramid? 504 units² 864 units² 1,080 units² 2,160 units²

Explanation:

Step1: Calculate base - area

The base is a square with side length $s = 12$. The area of the base $B=s^{2}=12^{2}=144$.

Step2: Calculate area of one triangular face

The formula for the area of a triangle is $A_{\triangle}=\frac{1}{2}bh$, where the base $b = 12$ and the slant - height $h = 15$. So $A_{\triangle}=\frac{1}{2}\times12\times15 = 90$.

Step3: Calculate total area of four triangular faces

Since there are 4 triangular faces, $A_{triangles}=4\times A_{\triangle}=4\times90 = 360$.

Step4: Calculate surface area

The surface area $SA$ of a square pyramid is the sum of the base - area and the area of the four triangular faces. So $SA=B + A_{triangles}=144+360 = 504$.

Answer:

504 units$^{2}$