Question

perimeter of shape f. perimeter = □ units area = ? shape f with dimensions: 7 units (left), 4 units (top), 3 units, 2 units, 2 units (right), 2 units, 2 units (bottom right), 4 units (bottom). number buttons: 8, 9, 0, ., -, x. enter √ button.

Explanation:

Step1: Analyze the shape's perimeter

To find the perimeter, we can use the method of translating the horizontal and vertical segments to form a rectangle. First, let's find the total length of the horizontal sides. The bottom and top horizontal sides: the main horizontal length (before the indentation) can be considered. Wait, actually, a better way is to calculate the sum of all outer sides. Let's list all the outer sides:

Vertical sides: Left side is 7 units. Right side: we have 2 units (top right small rectangle), then 3 units, then 2 units (middle right), then 2 units (bottom right small rectangle)? Wait, no, let's do it by moving the indentations. The horizontal length: if we move the right indentation's horizontal parts, the total horizontal length is \(4 + 2+ 4= 10\)? Wait, no, looking at the figure, the top horizontal segment is 4 units, then there's a 2 units (the indentation's top), then the bottom horizontal segment is 4 units, and the other horizontal segments? Wait, maybe a better approach is to calculate the perimeter by considering the shape as a rectangle with some adjustments, but actually, let's sum all the outer edges:

Top: 4 units (left top) + 2 units (middle top indentation's top) + 4 units (right top? No, wait the figure: let's parse the coordinates. Let's assume the left side is vertical with length 7. The bottom is horizontal with length \(4 + 2+ 4 = 10\)? Wait, no, the bottom horizontal segment is 4 units (left bottom) + 2 units (middle bottom indentation's bottom) + 4 units (right bottom)? No, maybe I should look at the vertical and horizontal components.

Wait, the perimeter of a polygon is the sum of all its side lengths. Let's list all the sides:

Starting from the top left corner, moving right: 4 units (top horizontal). Then down: 3 units. Then right: 2 units. Then down: 2 units. Then left: 2 units. Then down: 2 units. Then left: 4 units (bottom horizontal). Then up: 7 units (left vertical). Wait, no, that's not right. Wait, maybe the correct way is to use the "rectangle perimeter" method by shifting the indentations. The vertical height: the left side is 7 units. The horizontal length: if we shift the right indentation's horizontal parts, the total horizontal length is \(4 + 2+ 4 = 10\)? Wait, no, let's calculate the sum of all horizontal and vertical sides.

Horizontal sides (top and bottom):

Top: 4 (left) + 2 (middle top) + 4 (right)? No, wait the top horizontal segment is 4 units (from left to the start of the indentation), then the indentation's top is 2 units (rightward), then the remaining top? Wait, maybe the figure is a rectangle with length \(4 + 2 + 4 = 10\) and height 7, but with some indentations, but actually, when calculating perimeter, the indentations' horizontal and vertical sides add up. Wait, let's do it step by step:

Vertical sides:

Left side: 7 units (from bottom to top).

Right side: Let's see the vertical segments on the right: 3 units (top right, down), 2 units (middle right, down), 2 units (bottom right, down). Wait, no, that's not. Wait, the right side has three vertical segments: 3 units (top), 2 units (middle), 2 units (bottom). But also, the left side is 7 units, so 3 + 2 + 2 = 7, which matches. So vertical sides total: 7 (left) + 3 + 2 + 2 (right) = 14? No, perimeter is sum of all outer sides, so vertical sides: left (7) + right (7) = 14? Wait, no, because the right side has multiple segments, but when you sum them, 3 + 2 + 2 = 7, so vertical total is 7 + 7 = 14.

Horizontal sides:

Top: 4 (left top) + 2 (middle top indentation's top) + 4 (right top? No, wait the top horizontal segments: left top is 4 units, then the indentation's top is 2 units (rightward), then the remaining top? Wait, no, the bottom horizontal segments: left bottom is 4 units, then the indentation's bottom is 2 units (leftward), then the right bottom is 4 units? Wait, maybe the horizontal sides are: top (4 + 2 + 4) = 10, bottom (4 + 2 + 4) = 10. So horizontal total is 10 + 10 = 20.

Then total perimeter is vertical total + horizontal total = 14 + 20 = 34? Wait, no, that can't be. Wait, maybe I made a mistake. Let's use the standard method for irregular shapes: the perimeter is equal to the perimeter of the enclosing rectangle plus twice the length of the indentation's horizontal or vertical sides. Wait, the enclosing rectangle would have length \(4 + 2 + 4 = 10\) and height 7. The perimeter of the rectangle is \(2\times(10 + 7)= 34\). Wait, but is there any indentation? Wait, looking at the figure, the right side has a notch: the top notch is 3 units down, 2 units right, 2 units down, 2 units left, 2 units down? Wait, no, maybe the figure is a rectangle with length 10 (4 + 2 + 4) and height 7, but with a small rectangle removed? Wait, no, the area would be different, but for perimeter, when you have a notch, the perimeter increases by twice the length of the notch's horizontal or vertical sides. Wait, in this case, the notch: the horizontal part of the notch is 2 units (rightward), and the vertical parts are 3 units and 2 units? No, maybe I should re-express the shape.

Wait, let's list all the side lengths:

1. Top horizontal: 4 units (left to the start of the top notch)
2. Top notch right: 2 units (right)
3. Top notch down: 3 units (down)
4. Middle horizontal: 2 units (right)
5. Middle down: 2 units (down)
6. Bottom notch left: 2 units (left)
7. Bottom notch down: 2 units (down)? No, wait, the bottom horizontal: 4 units (left to the start of the bottom notch)
8. Bottom horizontal: 2 units (left, the bottom notch)
9. Bottom horizontal: 4 units (right)
10. Left vertical: 7 units (up)
11. Wait, this is getting confusing. Let's use the "shifting" method. For horizontal sides: the total length of all horizontal sides (top and bottom) is equal to 2 times the length of the base of the enclosing rectangle. The enclosing rectangle's length is \(4 + 2 + 4 = 10\), so top and bottom horizontal sides sum to \(2\times10 = 20\). For vertical sides: the total length of all vertical sides is equal to 2 times the height of the enclosing rectangle. The height is 7, so vertical sides sum to \(2\times7 = 14\). Then total perimeter is \(20 + 14 = 34\). Wait, but let's check with the given side lengths. The left vertical is 7, the right vertical segments: 3 + 2 + 2 = 7, so that's correct. The top horizontal: 4 + 2 + 4 = 10, bottom horizontal: 4 + 2 + 4 = 10, so total horizontal: 20, vertical: 14, total perimeter 34.

Wait, but maybe I made a mistake. Let's count again:

Horizontal sides:

- Top: 4 (left) + 2 (middle top) + 4 (right) = 10
- Bottom: 4 (left) + 2 (middle bottom) + 4 (right) = 10
Total horizontal: 10 + 10 = 20

Vertical sides:

- Left: 7
- Right: 3 (top right down) + 2 (middle right down) + 2 (bottom right down) = 7
Total vertical: 7 + 7 = 14

Perimeter: 20 + 14 = 34

Yes, that makes sense.

Answer:

34