Question

find the perimeter ( p ) of the given figure with side lengths 2 cm, 2 cm, 14 cm, 2 cm, 14 cm, 2 cm (from the image). ( p = square ) cm

Explanation:

Step1: Identify the shape's dimensions

The figure appears to be a rectangle (or a composite shape that can be analyzed as a rectangle) with length \( l = 14 + 2 = 16 \) cm? Wait, no, looking at the diagram, actually, let's re - examine. Wait, the horizontal sides: there are two 2 - cm segments and a 14 - cm? Wait, no, maybe it's a rectangle with length \( 14 + 2=16 \) cm? No, wait, the vertical sides: two 14 - cm and two 2 - cm? Wait, no, let's count the perimeter. The perimeter of a rectangle is \( P = 2\times( length + width) \). Wait, looking at the diagram, the total length (vertical) is \( 14 + 2=16 \) cm? No, wait, the horizontal sides: top is 2 cm, bottom is 2 cm, and the middle? Wait, maybe the shape is a rectangle with length \( 14 + 2 = 16 \) cm? No, wait, let's list all the sides. The outer sides: left side 14 cm, right side 14 cm, top side 2 cm, bottom side 2 cm, and then the two middle sides? Wait, no, maybe I misread. Wait, the figure is a composite of a square (2x2) and a rectangle (14x2), but when calculating the perimeter, we have to consider the outer edges. Wait, actually, if we "unfold" the shape, the total length of the horizontal sides: 2 + 2+2 + 2? No, wait, let's do it properly. The perimeter is the sum of all outer sides. Let's list each side:

Top: 2 cm

Right: 14 + 2=16 cm? No, right side: from top to bottom, it's 2 cm (top square) + 14 cm (rectangle) = 16 cm? Wait, no, the right side is 14 cm (the long part) and 2 cm (the top part)? Wait, no, looking at the diagram, the vertical sides: left side is 14 cm, right side is 14 cm, and then the top has a 2 - cm segment, bottom has a 2 - cm segment, and the two middle vertical segments? Wait, no, maybe the shape is a rectangle with length \( 14 + 2=16 \) cm and width 2 cm? No, that doesn't make sense. Wait, another approach: the perimeter of a rectangle is \( P = 2\times(l + w) \). Wait, maybe the total length (the longer side) is \( 14 + 2 = 16 \) cm and the width is 2 cm? No, wait, let's count the sides:

Horizontal sides: 2 cm (top), 2 cm (bottom), and two sides of 14 cm? No, I think I made a mistake. Wait, let's look at the diagram again. The figure has:

- Top horizontal side: 2 cm

- Right vertical side: 14 + 2 = 16 cm? No, right vertical side: from top to bottom, it's 2 cm (top square) + 14 cm (rectangle) = 16 cm

- Bottom horizontal side: 2 cm

- Left vertical side: 14 + 2 = 16 cm

- Then the two middle horizontal sides? Wait, no, the middle horizontal side (the one dividing the square and the rectangle) is internal, so we don't count it for perimeter.

Wait, so the perimeter is \( 2\times(16 + 2)=2\times18 = 36 \)? No, that can't be. Wait, maybe the length is 14 cm and the width is 2 + 2 = 4 cm? No, let's start over.

Wait, the figure is composed of a square (2x2) and a rectangle (14x2) attached vertically. When calculating the perimeter, the shared side (between the square and the rectangle) is internal, so we exclude it.

The perimeter of the square: \( 4\times2 = 8 \), but we lose 2 cm (the shared side). The perimeter of the rectangle: \( 2\times(14 + 2)=32 \), but we also lose 2 cm (the shared side). So total perimeter: \( 8 - 2+32 - 2=36 \)? Wait, no, that's not the right way. The correct way is to look at the outer edges.

Let's list all the outer edges:

- Top: 2 cm (from the square)

- Right: 14 + 2 = 16 cm (from the rectangle's right side and the square's right side)

- Bottom: 2 cm (from the rectangle's bottom)

- Left: 14 + 2 = 16 cm (from the rectangle's left side and the square's left side)

- Then the two horizontal edges on the left and right? Wait, no, I think I messed up. Wait, the correct dimensions: the total height (vertical) is 14 + 2 = 16 cm, and the total width (horizontal) is 2 cm? No, that would make it a rectangle of 16x2, perimeter \( 2\times(16 + 2)=36 \). Wait, but let's check again.

Wait, the square is 2x2, and the rectangle is 14x2. When we put them together vertically, the total height is 2 + 14 = 16 cm, and the width is 2 cm. So the perimeter is \( 2\times(16 + 2)=2\times18 = 36 \) cm.

Wait, another way: sum all the outer sides.

Top: 2 cm

Right: 14 + 2 = 16 cm

Bottom: 2 cm

Left: 14 + 2 = 16 cm

Wait, no, that's only four sides, but a rectangle has four sides. Wait, yes, a rectangle has two lengths and two widths. So length \( l = 16 \) cm, width \( w = 2 \) cm. Then \( P = 2\times(l + w)=2\times(16 + 2)=36 \) cm.

Step2: Calculate the perimeter

Using the formula for the perimeter of a rectangle \( P = 2\times( length + width) \). Here, length \( l=14 + 2 = 16 \) cm, width \( w = 2 \) cm.

\( P=2\times(16 + 2)=2\times18 = 36 \) cm.

Answer:

36