Question

what is the surface area of the regular pyramid below? a. 700 units² b. 1512 units² c. 756 units² d. 1124 units²

Explanation:

Step1: Calculate the base area

The base is a square with side length \(s = 14\). The area of the base \(B=s^{2}\), so \(B = 14\times14=196\).

Step2: Calculate the lateral - face area

Each lateral face is a triangle with base \(b = 14\) and height \(h = 18\). The area of a triangle is \(A_{\triangle}=\frac{1}{2}bh\). For one lateral face, \(A_{\triangle}=\frac{1}{2}\times14\times18 = 126\).
Since there are 4 lateral faces, the total lateral - surface area \(L = 4\times A_{\triangle}\). So \(L=4\times126 = 504\).

Step3: Calculate the total surface area

The surface area of a pyramid \(S=B + L\). Substitute \(B = 196\) and \(L = 504\) into the formula: \(S=196+504=700\).

Answer:

A. 700 units²