Let's solve the problem step by step.

1. Area of the Triangle

The formula for the area of a triangle is given by:

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

In the triangle shown:

• Base = 6 units
• Height = 8 units

$A_{\triangle} = \frac{1}{2} \times 6 \times 8 = \frac{1}{2} \times 48 = 24 \, \text{square units}$

2. Area of the Rectangle

The formula for the area of a rectangle is:

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

In the rectangle shown:

• Length = 13 units
• Width = 8 units

$A_{\text{rectangle}} = 13 \times 8 = 104 \, \text{square units}$

3. Total Area

Now, to find the total area of the trapezoid (which is composed of the triangle and the rectangle), we add the areas of the triangle and the rectangle:

$\text{Total Area} = A_{\triangle} + A_{\text{rectangle}} = 24 + 104 = 128 \, \text{square units}$

Final Answer:

• Area of the triangle: 24 square units
• Area of the rectangle: 104 square units
• Total area: 128 square units

Let me know if you'd like any further details or have any questions!

Related Questions:

1. How do you calculate the area of a trapezoid directly without dividing it into shapes?
2. How would the areas change if the triangle’s height were increased?
3. What happens to the total area if both the base of the triangle and the length of the rectangle are doubled?
4. How does the formula for the area of a triangle relate to that of a rectangle?
5. What other ways can you decompose a trapezoid into simpler shapes?

Tip:

Always make sure to label the base and height of the triangle correctly—these must be perpendicular to each other for the area formula to work!