Question

the solid below is made from 1 inch cubes. find the total surface area of the syour answer.

Explanation:

Step1: Count the number of faces on each side

• Front and Back:
• For the front - view:
• The lower part has \(4\times3 = 12\) squares. The upper part has \(3\) squares. So, the front - view has \(12 + 3=15\) squares.
• Since the back - view is the same as the front - view, the total number of squares for front and back is \(2\times15 = 30\).
• Left and Right:
• The left - view has \(4\times4 = 16\) squares. The right - view is the same as the left - view. So, the total number of squares for left and right is \(2\times16=32\).
• Top and Bottom:
• The top - view:
• The lower part has \(4\times3 = 12\) squares. The upper part has \(3\) squares. So, the top - view has \(12 + 3 = 15\) squares.
• Since the bottom - view is the same as the top - view, the total number of squares for top and bottom is \(2\times15=30\).

Step2: Calculate the surface area

• The area of each square is \(1\times1 = 1\) square inch.
• The total surface area \(A=(30 + 32+30)\times1\).

Answer:

\(92\) square inches.