The problem in the image asks to find the perimeter (keliling) of the figure shown, given that the length of $BD$ is 21 cm. Here are the details:

Analyzing the Figure:

The figure is composed of:

• A quadrilateral on the left side (trapezoid shape).
• A triangle $BCD$ on the right side.

The key information is:

• $AB = 25$ cm
• $BC = 20$ cm
• $CD = 12$ cm
• $DE = 7$ cm
• $EF = 12$ cm
• $AF$ is unknown (but from symmetry it looks equal to $AB$).
• $BD = 21$ cm (given)

Finding the Perimeter:

The perimeter is the sum of all the sides of the figure, which are:

• $AB = 25$ cm
• $BC = 20$ cm
• $CD = 12$ cm
• $DE = 7$ cm
• $EF = 12$ cm
• $FA = 25$ cm (assuming symmetry based on the shape)

So, the total perimeter is: $P = AB + BC + CD + DE + EF + FA$ $P = 25 + 20 + 12 + 7 + 12 + 25 = 101 \, \text{cm}$

Thus, the perimeter of the figure is 101 cm.

Let me know if you'd like more details or if you have any further questions!

Here are 5 related questions for further exploration:

1. How would you calculate the area of the triangle $BCD$ given its dimensions?
2. How would the perimeter change if the length of $BD$ were different?
3. How can you verify if the trapezoid on the left side is isosceles?
4. What formula would you use to calculate the area of the entire shape?
5. Can you use the Pythagorean theorem to confirm the length of any of the sides?

Tip: Always check for symmetry in shapes; it often simplifies perimeter calculations.