Question

find the lateral area of the triangular prism. 20 cm 32 cm 12 cm 16 cm square centimeters

Explanation:

Step1: Identify side - lengths of the base triangle

The base triangle has side - lengths 12 cm, 16 cm, and $\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}=20$ cm.

Step2: Recall the formula for the lateral area of a prism

The lateral area $L$ of a prism is given by $L = Ph$, where $P$ is the perimeter of the base and $h$ is the height of the prism. The height of the prism $h = 32$ cm.

Step3: Calculate the perimeter of the base triangle

$P=12 + 16+20=48$ cm.

Step4: Calculate the lateral area

$L = Ph=48\times32 = 1536$ $cm^{2}$.

Answer:

1536