Question

in the rhombus, ac = 2 cm, and db = 4 cm, then the area of the rhombus is:

Explanation:

Step1: Recall the formula for the area of a rhombus

The area of a rhombus is given by the formula \( A=\frac{1}{2} \times d_1 \times d_2 \), where \( d_1 \) and \( d_2 \) are the lengths of the diagonals.

Step2: Identify the diagonals

Here, \( d_1 = AC = 2 \, \text{cm} \) and \( d_2 = DB = 4 \, \text{cm} \).

Step3: Substitute the values into the formula

Substitute \( d_1 = 2 \) and \( d_2 = 4 \) into the formula:
\( A=\frac{1}{2} \times 2 \times 4 \)

Step4: Calculate the area

First, multiply \( 2 \) and \( 4 \): \( 2\times4 = 8 \). Then, multiply by \( \frac{1}{2} \): \( \frac{1}{2}\times8 = 4 \).

Answer:

The area of the rhombus is \( 4 \, \text{cm}^2 \).