Question

what is the perimeter of the figure shown if the slanted side is 10.6 units long?

the perimeter is \\(\square\\) units.
(type an integer or a decimal.)

Explanation:

Step1: Determine vertical side length

Assume each grid square has side length 1. The vertical side (height) spans 8 units (counting grid squares). So vertical side length = 8.

Step2: Determine bottom horizontal side length

Count grid squares for the bottom base: it spans 16 units. So bottom length = 16.

Step3: Determine top horizontal side length

Count grid squares for the top base: it spans 10 units. So top length = 10.

Step4: Sum all sides for perimeter

Perimeter = top length + vertical side + bottom length + slanted side + (other vertical side, but wait, no—wait, the figure is a trapezoid? Wait, looking at the grid: left side is vertical (8 units), top is 10, bottom is 16, right side is slanted (10.6), and wait, no—wait, the figure has four sides? Wait, no, let's re-examine. Wait, the figure: left vertical (8), top horizontal (10), right slanted (10.6), bottom horizontal (16), and wait, no—wait, maybe it's a pentagon? No, looking at the grid, the left is vertical (8 units), top is 10 units (horizontal), then a slanted side? Wait, no, the figure: let's count the sides. Left: 8 units (vertical). Top: 10 units (horizontal). Then a slanted side (10.6), then bottom: 16 units (horizontal), then left vertical? Wait, no, perimeter is sum of all outer sides. So sides: left (8), top (10), slanted (10.6), bottom (16), and wait, no—wait, the left side is vertical (8), top is 10, then the slanted side (10.6), then bottom is 16, and then the right vertical? No, no, the figure is a trapezoid? Wait, no, the grid: let's count the horizontal and vertical. Let's assume each grid is 1 unit. So left side: from bottom to top, 8 units (so length 8). Top side: 10 units (horizontal). Then the slanted side: 10.6. Bottom side: 16 units (horizontal). Then the right side? Wait, no, the figure has four sides? Wait, no, maybe I miscounted. Wait, the figure: left vertical (8), top horizontal (10), right slanted (10.6), bottom horizontal (16), and then the left vertical? No, perimeter is sum of all outer edges. Wait, no, the figure is a polygon with sides: left (8), top (10), slanted (10.6), bottom (16), and wait, no—wait, the left side is vertical (8), top is 10, then the slanted side (10.6), then bottom is 16, and then the right vertical? No, that can't be. Wait, maybe the figure is a trapezoid with left vertical (8), top (10), bottom (16), and right slanted (10.6), and also the left vertical? No, no, perimeter is sum of all sides. Wait, let's list all sides:

- Left vertical: 8 units (length 8)
- Top horizontal: 10 units (length 10)
- Slanted side: 10.6 units (given)
- Bottom horizontal: 16 units (length 16)
- Wait, but is there another vertical side? No, wait, the figure is a quadrilateral? Wait, no, looking at the grid, the left is vertical (8), top is 10, then a slanted side down to the bottom right, then bottom back to left. Wait, so the sides are: left (8), top (10), slanted (10.6), bottom (16). Wait, that's four sides? Wait, no, 8 + 10 + 10.6 + 16? Wait, no, that would be 8 + 10 + 10.6 + 16 = 44.6? Wait, no, wait, maybe the left side is 8, top is 10, slanted is 10.6, bottom is 16, and also the right vertical? No, no, the slanted side is the right side. Wait, let's check again. Let's count the grid squares:

- Vertical side (left): from bottom to top, 8 squares, so length 8.
- Top horizontal: 10 squares, length 10.
- Slanted side: given as 10.6.
- Bottom horizontal: 16 squares, length 16.
- Wait, but is there another side? No, the figure is a quadrilateral with sides: left (8), top (10), right (10.6), bottom (16). So perimeter is 8 + 10 + 10.6 + 16.

Step5: Calculate the sum

8 + 10 = 18; 18 + 10.6 = 28.6; 28.6 + 16 = 44.6.

Answer:

44.6