To find the area of the composite shape, we will divide it into two distinct parts: the triangular portion (Area 1) and the rectangular portion. Here's how to calculate the area:

Step 1: Area of the rectangle

The dimensions of the rectangle are:

• Width: $15 \, \text{cm}$
• Height: $8 \, \text{cm}$

The formula for the area of a rectangle is: $\text{Area of rectangle} = \text{width} \times \text{height}$ $\text{Area of rectangle} = 15 \times 8 = 120 \, \text{cm}^2$

Step 2: Area of the triangle

The triangle's base is $15 \, \text{cm}$ (same as the rectangle), and its height is the difference between $14 \, \text{cm}$ and $8 \, \text{cm}$: $\text{Height of triangle} = 14 - 8 = 6 \, \text{cm}$

The formula for the area of a triangle is: $\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Area of triangle} = \frac{1}{2} \times 15 \times 6 = 45 \, \text{cm}^2$

Step 3: Total area of the composite shape

Now, sum the areas of the rectangle and the triangle: $\text{Total area} = \text{Area of rectangle} + \text{Area of triangle}$ $\text{Total area} = 120 + 45 = 165 \, \text{cm}^2$

Final Answer:

The total area of the composite shape is: $165 \, \text{cm}^2$

Would you like further details or have additional questions?

Here are 5 follow-up questions you might find interesting:

1. How can we calculate the perimeter of this composite shape?
2. What happens if the height of the rectangle is changed? How does it affect the total area?
3. How can we find the diagonal length of the rectangle?
4. What if the triangular part is an isosceles triangle? How can we confirm that from the given measurements?
5. Can we rearrange the triangle and rectangle to form a square or other shapes of equal area?

Tip: When solving composite shape problems, always divide the shape into simpler components like rectangles, triangles, or circles for easier calculations.