To find the area of a rhombus when the lengths of its diagonals are given, we can use the following formula:
[tex]\[ \text{Area} = \frac{1}{2} \times d_1 \times d_2 \][/tex]
where [tex]\( d_1 \)[/tex] and [tex]\( d_2 \)[/tex] are the lengths of the diagonals of the rhombus.
Given:
- [tex]\( d_1 = 15 \)[/tex] cm (length of the first diagonal)
- [tex]\( d_2 = 36 \)[/tex] cm (length of the second diagonal)
Plugging these values into the formula, we get:
[tex]\[ \text{Area} = \frac{1}{2} \times 15 \times 36 \][/tex]
First, calculate the product of the diagonals:
[tex]\[ 15 \times 36 = 540 \][/tex]
Next, divide this product by 2 to find the area:
[tex]\[ \frac{540}{2} = 270 \][/tex]
Therefore, the area of the rhombus is:
[tex]\[ 270 \, \text{cm}^2 \][/tex]
