To solve this problem, we need to determine the area of the entire rectangle given that the area of the triangle is $14 \, \text{cm}^2$ and the base of the rectangle is $7 \, \text{cm}$.

Steps to Solve

1. Identify the Dimensions of the Triangle:

   • Since the area of the triangle is given as $14 \, \text{cm}^2$ and the triangle is within the rectangle, we assume the base of the triangle is the same as the width of the rectangle, which is $7 \, \text{cm}$.
   • The formula for the area of a triangle is: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$
   • Plugging in the area and the base, we get: $14 = \frac{1}{2} \times 7 \times \text{height}$
   • Solving for the height: $\text{height} = \frac{14 \times 2}{7} = 4 \, \text{cm}$

2. Calculate the Area of the Rectangle:

   • Now that we know the height of the rectangle is $4 \, \text{cm}$ and the width is $7 \, \text{cm}$, we can calculate the area of the rectangle using the formula: $\text{Area of Rectangle} = \text{width} \times \text{height} = 7 \times 4 = 28 \, \text{cm}^2$

Answer

The area of the whole rectangle is $28 \, \text{cm}^2$.

Would you like further clarification or details on any part of this solution?

Here are some related questions that might interest you:

1. How do we find the area of different shapes like circles or trapezoids?
2. What are the properties of triangles within rectangles?
3. Can you explain the different types of triangles and their area formulas?
4. How can we find unknown dimensions of a shape given its area?
5. What is the relationship between perimeter and area for rectangles?

Tip: When calculating areas, always check if units are consistent across all dimensions.