Answer:
[tex]50\text{ cm}^2[/tex]
Step-by-step explanation:
The area of a rhombus is defined as:
[tex]A=\dfrac{p\cdot q}{2}[/tex]
where p and q are the lengths of the rhombus' diagonals.
Since this rhombus is composed of 45-45-90 triangles, we know that both diagonals are equal. We can solve for the length of each diagonal by doubling the given half-diagonal:
[tex]p = 2 \cdot 5 = 10\text{ cm}[/tex]
So, the area of the rhombus is:
[tex]A=\dfrac{(10\text{ cm})^2}{2}[/tex]
[tex]A = \dfrac{100\text{ cm}^2}{2}[/tex]
[tex]\boxed{A=50\text{ cm}^2}[/tex]
