Question

what is the surface area of this triangular prism? 4 cm 16 cm 5 cm 3 cm square centimeters

Explanation:

Step1: Calculate area of triangular faces

The area of a triangle is $A=\frac{1}{2}bh$. Here, $b = 3$ cm and $h=4$ cm. So the area of one - triangular face is $A_{triangle}=\frac{1}{2}\times3\times4 = 6$ square cm. Since there are 2 triangular faces, the total area of triangular faces is $2\times6=12$ square cm.

Step2: Calculate area of rectangular faces

There are 3 rectangular faces.
For the face with dimensions 3 cm and 16 cm, its area $A_1=3\times16 = 48$ square cm.
For the face with dimensions 4 cm and 16 cm, its area $A_2=4\times16 = 64$ square cm.
For the face with dimensions 5 cm and 16 cm, its area $A_3=5\times16 = 80$ square cm.
The total area of rectangular faces is $A_{rectangles}=48 + 64+80=192$ square cm.

Step3: Calculate total surface area

The total surface area of the triangular prism is the sum of the area of triangular faces and rectangular faces. So $A = 12+192=204$ square cm.

Answer:

204