Question

answer attempt limit of 2 cm² submit answer

Explanation:

Step1: Identify the shape

The shape is a square - based pyramid. The base is a square with side length $a = 3$ cm and the slant height $l=3$ cm.

Step2: Calculate the base area

The area of the base $B=a^{2}$, where $a = 3$ cm. So $B = 3^{2}=9$ $cm^{2}$.

Step3: Calculate the lateral - surface area

The lateral - surface area of a square - based pyramid with slant height $l$ and base side length $a$ is $4\times(\frac{1}{2}al)$. Here, $a = 3$ cm and $l = 3$ cm. So the lateral - surface area $L=4\times\frac{1}{2}\times3\times3=18$ $cm^{2}$.

Step4: Calculate the total surface area

The total surface area $S = B+L$. Substitute $B = 9$ $cm^{2}$ and $L = 18$ $cm^{2}$ into the formula. So $S=9 + 18=27$ $cm^{2}$.

Answer:

$27$