To calculate the area of this shaded shape, let's analyze it step-by-step.

This shape can be split into two parts:

1. A large right triangle.
2. A smaller right triangle at the top left corner.

Step 1: Area of the Large Triangle

The large triangle has:

• Base = 9.4 cm
• Height = 8 cm

Using the area formula for a triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Area}_{\text{large}} = \frac{1}{2} \times 9.4 \, \text{cm} \times 8 \, \text{cm} = 37.6 \, \text{cm}^2$

Step 2: Area of the Small Triangle

The small triangle has:

• Base = 2.4 cm
• Height = 1.8 cm

Applying the triangle area formula again: $\text{Area}_{\text{small}} = \frac{1}{2} \times 2.4 \, \text{cm} \times 1.8 \, \text{cm} = 2.16 \, \text{cm}^2$

Step 3: Subtract the Area of the Small Triangle from the Large Triangle

Since the shaded area is the large triangle minus the small triangle: $\text{Shaded Area} = \text{Area}_{\text{large}} - \text{Area}_{\text{small}}$ $\text{Shaded Area} = 37.6 \, \text{cm}^2 - 2.16 \, \text{cm}^2 = 35.44 \, \text{cm}^2$

Answer

The area of the shaded shape is: $35.44 \, \text{cm}^2$

Would you like a more detailed breakdown or have any questions?

Here are some related questions to explore:

1. How do you find the area of composite shapes with more complex structures?
2. How would the area calculation change if the shape included a circular segment?
3. Can the Pythagorean theorem verify the diagonal length of a right triangle in similar problems?
4. What methods can be used to approximate the area of irregular shapes?
5. How can understanding shapes help in real-world area calculations, like in architecture?

Tip: When working with composite shapes, breaking them down into simpler parts (like triangles or rectangles) makes it easier to calculate areas accurately.