To determine the total area of the figure, we first divide it into a rectangle and a triangle, as shown in the problem.

Step 1: Find the dimensions of the rectangle and triangle

• Rectangle:

  • Width = 3 units (horizontal length)
  • Height = 1 unit (vertical height)

• Triangle (below the rectangle):

  • Base = 3 units (same as the rectangle's width)
  • Height = 3 units (vertical distance from the rectangle's bottom to the triangle's tip)

Step 2: Calculate the area of the rectangle

The formula for the area of a rectangle is:
$\text{Area} = \text{Width} \times \text{Height}$
Substitute the values:
$\text{Area} = 3 \times 1 = 3 \, \text{square units.}$

Step 3: Calculate the area of the triangle

The formula for the area of a triangle is:
$\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}$
Substitute the values:
$\text{Area} = \frac{1}{2} \times 3 \times 3 = \frac{9}{2} = 4.5 \, \text{square units.}$

Step 4: Total area of the figure

The total area is the sum of the rectangle's and triangle's areas:
$\text{Total Area} = 3 + 4.5 = 7.5 \, \text{square units.}$

Final Answers:

• Area of the rectangle = 3 square units
• Area of the triangle = 4.5 square units
• Area of the figure = 7.5 square units

Would you like a detailed explanation for any step?

Related Questions:

1. How do you find the area of other composite figures like trapezoids or parallelograms?
2. What is the formula for the area of a trapezoid, and how does it relate to this problem?
3. How do you calculate areas on a grid without formulas?
4. Can this figure's area be verified using another method?
5. What happens if the units are scaled to a different size?

Tip:

Always break complex shapes into simpler ones (rectangles, triangles, etc.) to calculate their areas step by step.