https://file.aiquickdraw.com/mathbot/file/1726753216166jq0wp0y8.jpg

Let's break down the compound shape to find the value of \(x\).

### Step 1: Divide the compound shape into two rectangles.
The compound shape can be split into two rectangles:

- **Rectangle 1**: The larger bottom rectangle with dimensions 10 cm by 6 cm.
- **Rectangle 2**: The smaller top-right rectangle with dimensions \(x\) cm by 3 cm.

### Step 2: Express the total area.
The total area of the shape is given as 75 cm². The area of each rectangle can be calculated as follows:

- **Area of Rectangle 1**: \( \text{Area} = \text{length} \times \text{width} = 10 \times 6 = 60 \, \text{cm}^2 \).
- **Area of Rectangle 2**: \( \text{Area} = x \times 3 = 3x \, \text{cm}^2 \).

Thus, the total area of the compound shape is:
\[
60 + 3x = 75
\]

### Step 3: Solve for \(x\).
Now, we solve for \(x\):

\[
60 + 3x = 75
\]
\[
3x = 75 - 60
\]
\[
3x = 15
\]
\[
x = \frac{15}{3} = 5
\]

Thus, the value of \(x\) is **5 cm**.

Let me know if you'd like more details on this, or if you have any other questions!

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Here are some related questions for practice:
1. How do you calculate the area of a triangle?
2. What is the area of a rectangle with dimensions 7 cm by 9 cm?
3. If the area of a rectangle is 45 cm² and its length is 9 cm, what is the width?
4. How do you find the perimeter of a compound shape?
5. What is the formula for finding the area of a circle?

**Tip**: Always break down compound shapes into simple geometric figures to make area calculations easier!

The area of the compound shape below is 75 cm². Find the value of x.

Solve for the missing value x in a compound shape where the total area is 75 cm². This problem involves algebra and geometry, using the formula for the area of a rectangle. Suitable for Grades 6-8.

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