Question

what is the surface area of this triangular prism? 17 cm 15 cm 17 cm 16 cm 12 cm square centimeters

Explanation:

Step1: Calculate area of triangular faces

The area of a triangle is $A=\frac{1}{2}bh$. For the triangular faces of the prism, $b = 16$ cm and $h=15$ cm. So the area of one - triangular face is $A_{triangle}=\frac{1}{2}\times16\times15= 120$ $cm^{2}$. The total area of the two triangular faces is $2\times120 = 240$ $cm^{2}$.

Step2: Calculate area of rectangular faces

There are three rectangular faces.
Face 1: With dimensions $12$ cm and $17$ cm, area $A_1=12\times17 = 204$ $cm^{2}$.
Face 2: With dimensions $12$ cm and $17$ cm, area $A_2=12\times17 = 204$ $cm^{2}$.
Face 3: With dimensions $12$ cm and $16$ cm, area $A_3=12\times16 = 192$ $cm^{2}$.
The total area of the rectangular faces is $A_{rectangles}=204 + 204+192=600$ $cm^{2}$.

Step3: Calculate total surface area

The surface area of the triangular prism $A = A_{triangles}+A_{rectangles}=240 + 600=840$ $cm^{2}$.

Answer:

840