Question

what is the surface area of the regular pyramid below? 19 16 16 a. 756 units² b. 864 units² c. 952 units² d. 856 units²

Explanation:

Step1: Calculate base - area

The base is a square with side length $s = 16$. The area of the base $B$ is given by $B=s^{2}=16^{2}=256$.

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 $b = 16$ and the height $h = 19$. So $A_{\triangle}=\frac{1}{2}\times16\times19 = 152$.

Step3: Calculate total area of triangular faces

A square - based pyramid has 4 triangular faces. The total area of the triangular faces $A_{triangles}=4\times A_{\triangle}=4\times152 = 608$.

Step4: Calculate surface area

The surface area $SA$ of the pyramid is the sum of the base - area and the total area of the triangular faces. So $SA=B + A_{triangles}=256+608=864$.

Answer:

B. 864 units²