Question

what is the surface area of this triangular prism? 16 mm 20 mm 6.5 mm 12 mm square millimeters

Explanation:

Step1: Calculate area of triangular faces

The formula for the area of a triangle is $A=\frac{1}{2}bh$. Here, $b = 12$ mm and $h=6.5$ mm. So, $A_{triangle}=\frac{1}{2}\times12\times6.5 = 39$ square - mm. Since there are 2 triangular faces, the total area of triangular faces is $2\times39=78$ square - mm.

Step2: Calculate area of first rectangular face

One rectangular face has dimensions 12 mm (base of triangle) and 16 mm. So its area $A_1 = 12\times16=192$ square - mm.

Step3: Calculate area of second rectangular face

Another rectangular face has dimensions 6.5 mm (height of triangle) and 16 mm. So its area $A_2 = 6.5\times16 = 104$ square - mm.

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions 20 mm (slant - side of triangle) and 16 mm. So its area $A_3 = 20\times16=320$ square - mm.

Step5: Calculate total surface area

The total surface area $A$ of the triangular prism is the sum of the areas of the 2 triangular faces and 3 rectangular faces. $A=78 + 192+104 + 320=694$ square - mm.

Answer:

694