Question

what is the surface area of the rec square millimeters

Explanation:

Step1: Identify the dimensions of the rectangular - prism parts

The rectangular - prism has three pairs of faces. The dimensions of the faces are:

• Two faces with dimensions \(10\times5\) mm.
• Two faces with dimensions \(10\times3\) mm.
• Two faces with dimensions \(5\times3\) mm.

Step2: Calculate the area of each pair of faces

For the faces with dimensions \(10\times5\):
The area of one face is \(A_1 = 10\times5=50\) square mm. The area of two such faces is \(2\times A_1=2\times50 = 100\) square mm.
For the faces with dimensions \(10\times3\):
The area of one face is \(A_2=10\times3 = 30\) square mm. The area of two such faces is \(2\times A_2=2\times30=60\) square mm.
For the faces with dimensions \(5\times3\):
The area of one face is \(A_3 = 5\times3=15\) square mm. The area of two such faces is \(2\times A_3=2\times15 = 30\) square mm.

Step3: Calculate the total surface area

The total surface area \(S\) of the rectangular - prism is the sum of the areas of all six faces.
\(S=100 + 60+30=190\) square mm.

Answer:

190