To calculate the area of this compound shape, we need to break it into two simpler parts: a rectangle at the top and a triangle at the bottom.

Step 1: Area of the Rectangle

The rectangle's dimensions are:

• Width = 12 cm
• Height = 10 cm

The area of the rectangle is calculated using the formula: $\text{Area of rectangle} = \text{width} \times \text{height}$ $\text{Area of rectangle} = 12 \, \text{cm} \times 10 \, \text{cm} = 120 \, \text{cm}^2$

Step 2: Area of the Triangle

The triangle's base and height are:

• Base = 12 cm (same as the width of the rectangle)
• Height = 8 cm

The area of a triangle is calculated using the formula: $\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Area of triangle} = \frac{1}{2} \times 12 \, \text{cm} \times 8 \, \text{cm} = 48 \, \text{cm}^2$

Step 3: Total Area

The total area of the compound shape is the sum of the areas of the rectangle and the triangle: $\text{Total area} = \text{Area of rectangle} + \text{Area of triangle}$ $\text{Total area} = 120 \, \text{cm}^2 + 48 \, \text{cm}^2 = 168 \, \text{cm}^2$

Final Answer:

The area of the compound shape is: $\boxed{168 \, \text{cm}^2}$

Would you like further clarification or assistance with a similar problem?

Related Questions:

1. How would the area change if the dimensions of the rectangle were doubled?
2. What is the perimeter of the compound shape?
3. How do you calculate the area if the triangle was a right triangle with a different base-to-height ratio?
4. Can you find the area of irregular shapes using a grid?
5. What if the triangle was equilateral, how would that change the calculation?

Tip: Always visualize complex shapes as simpler components to make area calculations easier.