Answer:
Total lateral surface of the pyramid is: [tex]11.25 \,\,cm^2[/tex]
which agrees with the second option shown among the list of possible answers
Step-by-step explanation:
The total surface area of this square based pyramid consists of the addition of four triangles (the four lateral faces) of base 1.5 cm and height 3 cm, plus the area of its square base (1.5 cm x 1.5 cm).
Recall that the area of a triangle is defined as the product of its base time its height, divided by two. So the total surface for this pyramid is:
[tex]Total\,\,Area= 4\,*\,Area_{triangle}+Area_{square}\\Total\,\,Area= 4\,* \frac{1.5\,*\,3\,}{2} +1.5^2\\Total\,\,Area= 9\,+2.25 \,\,cm^2\\Total\,\,Area= 11.25 \,\,cm^2[/tex]
