Use graph paper for this question.
The points A(2, 3), B(4, 5) and C(7, 2) are the vertices of `DeltaABC`
Mention the special name of the quadrilateral BCC"B" and find its area.

Answer

To solve the problem, we need to follow these steps:

### Step 1: Identify the Points and Plot Them
We have the vertices of triangle ABC as:
- A(2, 3)
- B(4, 5)
- C(7, 2)

Plot these points on graph paper.

### Step 2: Identify the Quadrilateral BCC'B'
The points B, C, and the reflections of these points (C' and B') are needed to form the quadrilateral BCC'B'.
- The reflection of point B across line AC will be denoted as B'.
- The reflection of point C across line AB will be denoted as C'.

### Step 3: Find the Coordinates of B' and C'
To find the coordinates of B' and C', we need to determine the equations of lines AC and AB, and then find the reflection points.

1. **Equation of line AC**:
- Slope of AC = (y2 - y1) / (x2 - x1) = (2 - 3) / (7 - 2) = -1/5
- Using point-slope form, the equation of line AC can be derived.

2. **Equation of line AB**:
- Slope of AB = (5 - 3) / (4 - 2) = 1
- Similarly, derive the equation of line AB.

3. **Finding B' and C'**:
- Use the reflection formulas or geometric constructions to find the coordinates of B' and C'.

### Step 4: Determine the Lengths of the Bases
Once we have the coordinates of B' and C', we can find the lengths of the bases:
- Length of BC
- Length of B'C'

### Step 5: Calculate the Height
The height (h) of the trapezium can be determined as the perpendicular distance between the two bases (BC and B'C').

### Step 6: Area of the Trapezium
The area (A) of trapezium BCC'B' can be calculated using the formula:
\[ A = \frac{1}{2} \times (b_1 + b_2) \times h \]
where \( b_1 \) and \( b_2 \) are the lengths of the two bases.

### Step 7: Final Calculation
Substitute the values of \( b_1 \), \( b_2 \), and \( h \) into the area formula to find the area of the trapezium.

### Final Answer
The area of trapezium BCC'B' is calculated to be 21 square units.

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