https://file.aiquickdraw.com/mathbot/file/17255491420389fojoa1m.jpg

To calculate the area of the figure, we can break it down into smaller, simpler shapes like rectangles and then sum their areas. Let's analyze the shape:

1. The total width of the figure is given as **10.5 cm**.
2. The height of each vertical section (marked with arrows) is **3.4 cm** and the horizontal thickness of the figure is **1.2 cm**.

We can treat the figure as composed of three rectangles:
- **Top horizontal rectangle**: Width = 10.5 cm, Height = 1.2 cm.
- **Middle vertical rectangle**: Height = 3.4 cm, Width = 1.2 cm (as it extends vertically down).
- **Bottom horizontal rectangle**: Again, Width = 10.5 cm, Height = 1.2 cm.

### Calculation:
1. **Top rectangle area** = \( \text{Width} \times \text{Height} = 10.5 \, \text{cm} \times 1.2 \, \text{cm} = 12.6 \, \text{cm}^2 \).
2. **Middle rectangle area** = \( 3.4 \, \text{cm} \times 1.2 \, \text{cm} = 4.08 \, \text{cm}^2 \).
3. **Bottom rectangle area** = \( 10.5 \, \text{cm} \times 1.2 \, \text{cm} = 12.6 \, \text{cm}^2 \).

Finally, the total area of the figure is:
\[
\text{Total Area} = 12.6 \, \text{cm}^2 + 4.08 \, \text{cm}^2 + 12.6 \, \text{cm}^2 = 29.28 \, \text{cm}^2.
\]

Thus, the area of the figure is **29.28 cm²**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the area change if the thickness (1.2 cm) were doubled?
2. Can you calculate the perimeter of this shape?
3. How does breaking shapes into simpler components help with area calculations?
4. What is the formula for the area of complex figures?
5. How can we apply the concept of area to irregular figures?

**Tip:** For composite shapes, breaking them into smaller rectangles or squares simplifies area calculations greatly!

Find the area of the figure shown in the image.

Learn how to find the area of a composite shape made of three rectangles. This step-by-step guide covers the process of calculating individual rectangle areas and summing them to get the total area. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation