Area of a Rhombus: Applying the formula

Let's remember that there are two ways to calculate the area of a rhombus:

The first is the side times the height of the side.

The second is diagonal times diagonal divided by 2.

Since we are given both diagonals, we calculate it the second way:

$\frac{7\times4}{2}=\frac{28}{2}=14$

To solve this problem, we need to find the area of a rhombus given the lengths of its two diagonals.

Given Information:

• Main diagonal (longer diagonal): $d_1 = 7$ cm
• Secondary diagonal (shorter diagonal): $d_2 = 2$ cm

Formula for the Area of a Rhombus:
The area of a rhombus can be calculated using its diagonals with the formula: $A = \frac{1}{2} \times d_1 \times d_2$ where $d_1$ and $d_2$ are the lengths of the two diagonals.

Step-by-Step Solution:

Step 1: Identify the diagonal lengths
From the problem, we have:

• $d_1 = 7$ cm (main diagonal)
• $d_2 = 2$ cm (secondary diagonal)

Step 2: Apply the area formula
Substituting the values into the formula: $A = \frac{1}{2} \times 7 \times 2$

Step 3: Calculate the result
$A = \frac{1}{2} \times 14$ $A = 7 \text{ cm}^2$

Verification:
The diagonals of a rhombus bisect each other at right angles. The area formula $\frac{1}{2} \times d_1 \times d_2$ represents half the product of the diagonals, which geometrically divides the rhombus into four right triangles whose combined area equals the total area of the rhombus.

Therefore, the area of the rhombus is 7 cm².