Question

question
find the surface area of a square pyramid with side length 2 yd and slant height 2 yd.

Explanation:

Step1: Calculate base - area

The base is a square with side length $s = 2$ yd. The area of the base $B=s^{2}$. So, $B = 2^{2}=4$ square yards.

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 $b$ of the triangular face is the side - length of the square base ($b = 2$ yd) and the height is the slant height ($h = 2$ yd). So, $A_{\triangle}=\frac{1}{2}\times2\times2 = 2$ square yards.

Step3: Calculate total area of four triangular faces

Since there are 4 triangular faces, $A_{triangles}=4\times A_{\triangle}=4\times2 = 8$ square yards.

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, $SA=B + A_{triangles}=4 + 8=12$ square yards.

Answer:

12 square yards