Question

question 9
find the perimeter of the shaded region above.
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Explanation:

Step1: Identify the sides

The figure has two sides of length 4 (the slant sides), two sides of length 8 (the vertical sides), and one side of length 4 (the bottom side). Wait, no, let's count again. Wait, the shape is a combination: a rectangle with a triangle on top? Wait, no, looking at the lengths: the vertical sides are 8, the bottom is 4, the two slant sides are 4 each, and wait, the top triangle? Wait, no, maybe it's a pentagon? Wait, no, let's list all the outer sides. The perimeter is the sum of all outer sides. So the sides are: 8, 4, 8, 4, 4? Wait, no, let's see the diagram. The left vertical side: 8, bottom horizontal: 4, right vertical side: 8, then the two slant sides (the top triangle's two equal sides) each 4, and wait, is there a top horizontal side? No, because it's a triangle on top? Wait, no, maybe the shape is a rectangle with a triangle attached, but the perimeter would exclude the internal side (where the triangle and rectangle meet). Wait, the figure: left side 8, bottom 4, right side 8, then the two slant sides (each 4) and wait, maybe the top is a triangle, so the perimeter is left (8) + bottom (4) + right (8) + two slant sides (4 each) + wait, no, maybe I miscounted. Wait, let's look at the given lengths: the left vertical is 8, bottom horizontal 4, right vertical 8, and the two slant sides (the top) are 4 each, and is there a top horizontal? No, because it's a triangle. Wait, no, maybe the shape is a pentagon with sides: 8, 4, 8, 4, 4? Wait, no, let's add them up. Wait, the perimeter is the sum of all the outer edges. So: left side (8) + bottom (4) + right side (8) + the two slant sides (4 and 4). Wait, that's 8 + 4 + 8 + 4 + 4. Let's calculate that.

Step2: Sum the lengths

First, add the vertical sides: 8 + 8 = 16. Then the bottom: 4. Then the two slant sides: 4 + 4 = 8. Now total: 16 + 4 + 8 = 28? Wait, no, wait: 8 (left) + 4 (bottom) + 8 (right) + 4 (right slant) + 4 (left slant). Wait, 8 + 4 = 12, 12 + 8 = 20, 20 + 4 = 24, 24 + 4 = 28. Wait, is that correct? Let me check again. The figure: it's a rectangle with height 8 and width 4, and a triangle on top with two equal sides of 4. But when calculating perimeter, we don't include the side where the triangle and rectangle meet (the top of the rectangle, which is 4, but that's internal). So the outer sides are: left (8), bottom (4), right (8), and the two sides of the triangle (4 each). So that's 8 + 4 + 8 + 4 + 4 = 28.

Answer:

28