Question

find the surface area of this triangular prism. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate area of triangular faces

The triangular faces have base $b = 18$ cm and height $h = 24$ cm. The area of a triangle is $A_{triangle}=\frac{1}{2}bh$. So $A_{triangle}=\frac{1}{2}\times18\times24 = 216$ $cm^{2}$. Since there are 2 triangular faces, the total area of triangular faces is $2\times216=432$ $cm^{2}$.

Step2: Calculate area of rectangular faces

There are three rectangular faces.
Face 1: With dimensions 18 cm and 30 cm, area $A_1 = 18\times30=540$ $cm^{2}$.
Face 2: With dimensions 24 cm and 30 cm, area $A_2 = 24\times30 = 720$ $cm^{2}$.
Face 3: With dimensions 20 cm and 30 cm, area $A_3=20\times30 = 600$ $cm^{2}$.
The total area of rectangular faces is $A_{rect}=540 + 720+600=1860$ $cm^{2}$.

Step3: Calculate total surface area

The surface - area of the triangular prism is the sum of the area of the triangular faces and the area of the rectangular faces. So $A = 432+1860 = 2292$ $cm^{2}$.

Answer:

$2292$ $cm^{2}$