Question

a pyramid has a square base with side lengths of 10 centimeters. the slant height of the faces is 12 centimeters. what is the surface area of the pyramid? 200 cm² 240 cm² 500 cm² 340 cm²

Explanation:

Step1: Calculate base - area

The base is a square with side length $s = 10$ cm. The area of the base $B$ is given by $B=s^{2}$. So, $B = 10^{2}=100$ $cm^{2}$.

Step2: Calculate area of one triangular face

The area of a triangle is $A_{\triangle}=\frac{1}{2}\times base\times height$. Here, the base of each triangular face is the side - length of the square base ($b = 10$ cm) and the height is the slant height ($l = 12$ cm). So, $A_{\triangle}=\frac{1}{2}\times10\times12 = 60$ $cm^{2}$.

Step3: Calculate total area of triangular faces

A square - based pyramid has 4 triangular faces. The total area of the 4 triangular faces $A_{triangles}=4\times A_{\triangle}=4\times60 = 240$ $cm^{2}$.

Step4: Calculate total surface area

The total surface area $A$ of the pyramid is the sum of the base area and the total area of the triangular faces. So, $A=B + A_{triangles}=100+240 = 340$ $cm^{2}$.

Answer:

$340$ $cm^{2}$