Let's calculate the areas of Triangle A, Triangle B, and the whole figure.

Step 1: Area of Triangle A

The formula for the area of a triangle is:

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

For Triangle A:

• Base = 5 units
• Height = 3 units

$\text{Area of Triangle A} = \frac{1}{2} \times 5 \times 3 = \frac{15}{2} = 7.5 \, \text{square units}$

Step 2: Area of Triangle B

Similarly, for Triangle B:

• Base = 10 units
• Height = 3 units

$\text{Area of Triangle B} = \frac{1}{2} \times 10 \times 3 = \frac{30}{2} = 15 \, \text{square units}$

Step 3: Total Area of the Whole Figure (Trapezoid)

The original figure is a trapezoid with:

• Bases = 5 units and 10 units
• Height = 3 units

The formula for the area of a trapezoid is:

$\text{Area of Trapezoid} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$

$\text{Area of Trapezoid} = \frac{1}{2} \times (5 + 10) \times 3 = \frac{1}{2} \times 15 \times 3 = \frac{45}{2} = 22.5 \, \text{square units}$

Step 4: Confirming the Whole Area

Notice that the whole figure is composed of two triangles, A and B:

• Area of Triangle A = 7.5 square units
• Area of Triangle B = 15 square units

The sum of their areas:

$7.5 + 15 = 22.5 \, \text{square units}$

This matches the area of the trapezoid, confirming our calculations are consistent.

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Final Answer

Figure	Area (square units)
Triangle A	7.5
Triangle B	15
Whole figure	22.5

Would you like more details or further clarifications?

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5 Related Questions:

1. How do you derive the formula for the area of a trapezoid?
2. What other ways can a trapezoid be divided into smaller shapes?
3. How does changing the height of a trapezoid affect its area?
4. Can you generalize the solution for any trapezoid with unknown base lengths?
5. What happens to the area if the triangles overlap slightly?

Tip:

When working with composite figures, it's helpful to solve for individual parts to verify the total area systematically.