The image shows a composite figure. The goal is to find the perimeter of the figure. The figure consists of a rectangle on top and a smaller rectangle at the bottom, connected by vertical lines. The dimensions are given in centimeters. The top rectangle has a width of 52 cm and a height of 65 cm. The bottom rectangle has a width of 21 cm and a height of 28 cm.

1. Problem Description

The image shows a composite figure. The goal is to find the perimeter of the figure. The figure consists of a rectangle on top and a smaller rectangle at the bottom, connected by vertical lines. The dimensions are given in centimeters. The top rectangle has a width of 52 cm and a height of 65 cm. The bottom rectangle has a width of 21 cm and a height of 28 cm.

2. Solution Steps

First, let's consider the top rectangle.

The dimensions of the top rectangle are 52 cm and 65 cm.

Next, consider the bottom rectangle.

The dimensions of the bottom rectangle are 21 cm and 28 cm.

The height of the smaller rectangle is 28 cm, the width is 21 cm.

To find the perimeter, we need to calculate the length of each side of the figure and add them up.

The top side is 52 cm.

The left side of the upper rectangle is 65 cm. The height of lower rectangle is 28 cm. The width of the lower rectangle is 21 cm. Thus, we can see that from left side we have $65 + 28 + 21= 93$.

Since it is symmetrical, then the right side is also 93 cm.

Now, we need to consider the horizontal section which is touching the two rectangle:

The horizontal sides connecting top and bottom rectangles are calculated as:

$\frac{52-21}{2} = \frac{31}{2}= 15.5$ cm for both left and right horizontal sections.

The bottom side is 21 cm.

Therefore, the perimeter can be calculated as:

$52 + 65 + 15.5 + 28 + 21 + 28 + 15.5 + 65$

$= 52 + 65 + 65 + 28 + 28 + 21 + 15.5 + 15.5$

$= 52 + 130 + 56 + 21 + 31$

$= 52 + 130 + 56 + 52$

$= 52 + 52 + 130 + 56$

$= 104 + 186 = 290$ cm.

Alternative approach:

The perimeter consists of the top side (52 cm), the two vertical sides which are 65 + 28 = 93 cm each, and the bottom side (21 cm). We also need to account for the two horizontal segments connecting the rectangles. Each of these segments has a length of (52 - 21)/2 = 31/2 = 15.5 cm.

So the perimeter is 52 + 2 * 93 + 21 + 2 * 15.5 = 52 + 186 + 21 + 31 = 290 cm.

3. Final Answer

290 cm