https://file.aiquickdraw.com/mathbot/file/1729034695984tijorvj4.jpg

The shape in the image is a combination of a rectangle and a right-angled triangle, both of which contribute to the total area. Let's break down the calculation of the area.

1. **Rectangle**: 
   - The rectangle has dimensions of 7 cm by 8 cm.
   - Area of the rectangle = \( \text{length} \times \text{width} = 7 \, \text{cm} \times 8 \, \text{cm} = 56 \, \text{cm}^2 \).

2. **Right-angled Triangle**: 
   - The triangle's base and height are given as 2.4 cm and 1.8 cm, respectively.
   - Area of the triangle = \( \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2.4 \, \text{cm} \times 1.8 \, \text{cm} = 2.16 \, \text{cm}^2 \).

3. **Trapezoidal section**:
   - The remaining section is a right-angled trapezoid, which has one parallel side measuring 7 cm, the other parallel side being 9.4 cm, and the height of 1.8 cm.
   - Area of trapezoid = \( \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height} = \frac{1}{2} \times (7 + 9.4) \, \text{cm} \times 1.8 \, \text{cm} = 14.22 \, \text{cm}^2 \).

**Total Area**:
- Area = \( 56 \, \text{cm}^2 \) (rectangle) + \( 2.16 \, \text{cm}^2 \) (triangle) + \( 14.22 \, \text{cm}^2 \) (trapezoid)
- Total area ≈ \( 72.38 \, \text{cm}^2 \)

Would you like further details on this calculation? Here are 5 related questions to expand on this concept:

1. How would the total area change if the height of the rectangle were increased?
2. What is the perimeter of this combined shape?
3. Can you calculate the diagonal length of the rectangle using the Pythagorean theorem?
4. How does the area of the triangle change if the base doubles?
5. Can you calculate the area of a similar shape with different dimensions?

**Tip**: When dealing with composite shapes, always try to break them into simpler geometric figures like rectangles, triangles, or trapezoids to simplify area calculations.

Calculate the area of the composite shape consisting of a rectangle, triangle, and trapezoid as shown in the image.

Learn how to calculate the area of a composite shape consisting of a rectangle (7 cm by 8 cm), a triangle (base 2.4 cm, height 1.8 cm), and a trapezoid (bases 7 cm and 9.4 cm, height 1.8 cm). This detailed solution breaks down each shape and provides the total area of approximately 72.38 cm². Ideal for students in Grades 6-8.

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