The following figure is made of 
\[2\] triangles.
A quadrilateral with one pair of parallel sides.  The base lengths are 5 units and 10 units.  The height is 3 units. A dashed line from opposite vertices creates two triangles, labeled A and B. Triangle A has a base of 5 units and a height of 3 units. Triangle B has a base of 10 units and a height of 3 units.
\[5\]
\[10\]
\[3\]
Find the area of each part of the figure and the whole figure.
Figure	Area (square units)
Triangle A	
Triangle B	
Whole figure	


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.

---

### 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?

---

### 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.

The following figure is made of 2 triangles. A quadrilateral with one pair of parallel sides. The base lengths are 5 units and 10 units. The height is 3 units. A dashed line from opposite vertices creates two triangles, labeled A and B. Triangle A has a base of 5 units and a height of 3 units. Triangle B has a base of 10 units and a height of 3 units. Find the area of each part of the figure and the whole figure.

Find the areas of two triangles and a trapezoid with base lengths of 5 and 10 units and a height of 3 units. Learn how to calculate triangle and trapezoid areas using simple geometric formulas. Suitable for students in Grades 6-8.

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