From the perimeter, we could determine the side of the square base
4 × s = perimeter
4s = 48
s = 12
Half of the side is 6
See image attached
OPTION A
Find the slant height using pythagoras
sh = [tex] \sqrt{ 6^{2}+( \sqrt{13})^{2} } [/tex]
sh = [tex] \sqrt{36+13} [/tex]
sh = √49
sh = 7
The slant height is 7
OPTION B
The lateral area could be determined using formula of triangle area. There are 4 triangles
Lateral area = 4 × triangle area
Lateral area = 4 × 1/2 × b × h
Lateral area = 4 × 1/2 × 12 × 7
Lateral area = 168
OPTION C
Total area is the sum of lateral area and the base area (area of a square)
Total area = lateral area + base area
Total area = 168 + (s × s)
Total area = 168 + (12 × 12)
Total area = 168 + 144
Total area = 312
OPTION D
Volume = 1/3 × base area × altitude
Volume = 1/3 × 144 × √13
Volume = 48√13
