Answer:
Total lateral surface of the pyramid is:
![11.25 \,\,cm^2](https://img.qammunity.org/2021/formulas/mathematics/middle-school/aasxsc6dsut2bujrso8ctcapvi3uamrjb1.png)
which agrees with the second option shown among the list of possible answers
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:
![Total\,\,Area= 4\,*\,Area_(triangle)+Area_(square)\\Total\,\,Area= 4\,* (1.5\,*\,3\,)/(2) +1.5^2\\Total\,\,Area= 9\,+2.25 \,\,cm^2\\Total\,\,Area= 11.25 \,\,cm^2](https://img.qammunity.org/2021/formulas/mathematics/middle-school/ygbt3o3h5y19zf13b7hzoaa73uz6lgqfu9.png)