Let's break down the problem and calculate the area step by step.

1. Area of the rectangle (denoted by □):

The formula for the area of a rectangle is:

$A_{\text{rectangle}} = \text{length} \times \text{width}$

From the image:

• Length = 6 inches
• Width = 5 inches

So, the area of the rectangle is:

$A_{\text{rectangle}} = 6 \, \text{in} \times 5 \, \text{in} = 30 \, \text{in}^2$

2. Area of the triangle (denoted by △):

The formula for the area of a triangle is:

$A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}$

From the image:

• Base = 4 inches
• Height = 3 inches

So, the area of the triangle is:

$A_{\text{triangle}} = \frac{1}{2} \times 4 \, \text{in} \times 3 \, \text{in} = \frac{1}{2} \times 12 = 6 \, \text{in}^2$

3. Total area of the figure:

The figure is made up of the rectangle and the triangle. Therefore, the total area is the sum of the areas of both shapes:

$A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle}} = 30 \, \text{in}^2 + 6 \, \text{in}^2 = 36 \, \text{in}^2$

Final Results:

• Area of the rectangle: 30 in²
• Area of the triangle: 6 in²
• Total area of the figure: 36 in²

Would you like any more details on the process or have any questions?

Here are 5 related questions to explore:

1. How do you find the area of other polygons, like trapezoids?
2. Can the area formula for triangles apply to any type of triangle?
3. What happens if the base and height are not perpendicular in a triangle?
4. How would you find the area if the shapes were three-dimensional?
5. How can you check your work when calculating areas in composite figures?

Tip: Always check the units used for measurements to ensure consistency, especially when working with mixed shapes or dimensions.