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 $B$ is $B=s^2=12^2 = 144$.

Step2: Calculate area of one triangular face

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

Step3: Calculate total area of triangular faces

A square pyramid has 4 triangular faces. So the total area of the 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 total area of the triangular faces. So $SA=B + A_{triangles}=144+360=504$.

Answer:

504 units$^2$