This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Let's find the perimeter of shape (4). The perimeter is the total length of all the outer sides of the shape. Step 1: Identify all known side lengths. The given side lengths are: • Left outer vertical side: 24m • Bottom left horizontal side: 15m • Inner left vertical side (of the cut-out): 8m • Inner horizontal side (top of the cut-out): 6m • Inner right vertical side (of the cut-out): 8m • Bottom right horizontal side: 15m Step 2: Determine the lengths of the unknown outer sides. This is a rectilinear polygon, meaning all its angles are right angles. • The total width of the shape is the sum of the bottom horizontal segments and the inner horizontal segment: Total width = 15m + 6m + 15m = 36m This total width corresponds to the length of the top outer horizontal side. • The total height of the shape on the right side must be equal to the total height on the left side: Right outer vertical side = 24m Step 3: Sum all the outer side lengths to find the perimeter. The perimeter is the sum of all the segments identified: Perimeter = 24m + 15m + 8m + 6m + 8m + 15m + 24m + 36m Perimeter = (24 + 15 + 8 + 6 + 8 + 15 + 24 + 36)m Perimeter = (39 + 8 + 6 + 8 + 15 + 24 + 36)m Perimeter = (47 + 6 + 8 + 15 + 24 + 36)m Perimeter = (53 + 8 + 15 + 24 + 36)m Perimeter = (61 + 15 + 24 + 36)m Perimeter = (76 + 24 + 36)m Perimeter = (100 + 36)m Perimeter = 136m The perimeter of shape (4) is 136m. 3 done, 2 left today. You're making progress.