The area of the figure formed by joining the mid- points of the adjacent sides of a rhombus with diagonals of lengths 12 cm and 14 cm is

The problem involves finding the area of the figure formed by joining the midpoints of the adjacent sides of a rhombus, whose diagonals are 12 cm and 14 cm.

### Step-by-step solution:

1. **Area of the rhombus**: 
   The area of a rhombus can be calculated using the formula:
   \[
   \text{Area of rhombus} = \frac{1}{2} \times d_1 \times d_2
   \]
   where \( d_1 \) and \( d_2 \) are the lengths of the diagonals.

   Substituting the given values:
   \[
   \text{Area of rhombus} = \frac{1}{2} \times 12 \times 14 = 84 \, \text{cm}^2
   \]

2. **Figure formed by the midpoints**:
   When the midpoints of the adjacent sides of the rhombus are joined, the figure formed is a **rectangle**. This rectangle's area is one-half of the area of the original rhombus.

3. **Area of the rectangle**:
   Since the area of the rectangle is half of the area of the rhombus:
   \[
   \text{Area of rectangle} = \frac{1}{2} \times 84 = 42 \, \text{cm}^2
   \]

Thus, the area of the figure formed by joining the midpoints of the adjacent sides of the rhombus is \( \boxed{42} \, \text{cm}^2 \).

Would you like further details or have any other questions?

### Related Questions:
1. How do you find the area of a rhombus if the sides are given instead of the diagonals?
2. What is the perimeter of a rhombus with diagonals 12 cm and 14 cm?
3. How do you calculate the length of the sides of a rhombus from its diagonals?
4. What is the difference between the area of a rectangle and a rhombus with the same side lengths?
5. How does the figure change when the diagonals of a rhombus are equal?

### Tip:
When midpoints of adjacent sides of a quadrilateral are joined, the resulting figure will often be a rectangle or a parallelogram.

The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals of lengths 12 cm and 14 cm is

Find the area of the rectangle formed by joining the midpoints of the adjacent sides of a rhombus with diagonals 12 cm and 14 cm. This solution explains key geometry concepts and provides formulas for calculating the areas of rhombuses and rectangles. Suitable for Grades 8-10.

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