ANSWER
[tex]SA=64cm^2[/tex]
EXPLANATION
We are given the square pyramid in the question.
To find it, we will use the formula:
[tex]\begin{gathered} SA\text{ = }A\text{ + }\frac{1}{2}ps \\ \text{where A = area of the base} \\ p\text{ = perimeter }of\text{ base} \\ s\text{ = slant height} \end{gathered}[/tex]
From the question, the slant height, s, is 6 cm.
To find the area of base, we use:
A = L * L
where L = base length = 4cm
=> A = 4 * 4
A = 16 sq cm
To find the perimeter of the base, we use:
P = 4L
=> P = 4 * 4
P = 16 cm
Therefore, the surface area of the pyramid is:
[tex]\begin{gathered} SA\text{ = 16 + }\frac{1}{2}(16)(6) \\ SA\text{ = 16 + 48} \\ SA=64cm^2 \end{gathered}[/tex]
The surface area of the pyramid is 64 square centimetres.
