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This image shows a geometric figure involving a compound shape that includes two right triangles with angles of \( 45^\circ \) and a rectangle. The problem seems to involve determining the unknown lengths of the sides or the area of the entire figure.

### Information from the figure:
- The two outer triangles are isosceles right triangles, as they have two \( 45^\circ \) angles, which means their two legs are equal.
- The base of the rectangle is labeled as 6 units, and the height of each outer vertical side is given as 5 units.

Since the two right triangles have \( 45^\circ \) angles, they are 45°-45°-90° triangles. In such triangles, the two legs are equal in length, and the hypotenuse is \( \sqrt{2} \) times the length of a leg.

To break this down, let’s compute the length of the legs and solve for any other parts that might be relevant.

Do you want me to proceed with calculations, or do you have a specific question about the diagram?

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Here are 5 related questions you could consider:
1. How do you calculate the area of a 45°-45°-90° triangle?
2. What is the perimeter of the entire shape?
3. How would you find the total area of this compound shape?
4. How can you determine the length of the diagonal connecting the two 45°-45°-90° triangles?
5. How can the Pythagorean theorem be used to check the sides of the triangles?

**Tip:** In a 45°-45°-90° triangle, knowing one leg length can help you find all other sides using simple trigonometric ratios.

Determine the unknown sides or total area of the compound shape with two 45°-45°-90° triangles and a rectangle.

Learn how to find the area and perimeter of a geometric shape consisting of two 45°-45°-90° triangles and a rectangle. This problem involves applying the Pythagorean Theorem and the properties of special right triangles. Suitable for students in Grades 7-9.

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