Remember that the formula for the area of a rhombus is [tex] \dfrac{pq}{2} [/tex], where [tex] p [/tex] and [tex] q [/tex] are the diagonals of the rhombus.
We can already find that one diagonal has length 6 (based on the fact that the diagram shows that half of the diagonal is 3). However, we will need to find the length of the other diagonal in order to find the area.
Also note that the diagonals in a rhombus are perpendicular to each other, meaning that they form a right angle. Based on this fact, we can realize that a triangle forms with one side being the side of the rhombus (length 5), another side being one half of the unknown diagonal, and another side being half of the known diagonal (length 3). This right triangle has a hypotenuse of 5 and a smaller side of 3, which means that the other side must be 4. This can be determined by the Pythagorean Theorem (the length of the larger leg will be coined [tex] x [/tex]):
[tex] 3^2 + x^2 = 5^2 [/tex]
[tex] x^2 = 16 [/tex]
[tex] x = 4 [/tex]
Since we have determined one half of our unknown diagonal is 4, we can then realize that the length of the entire diagonal is 8. Using this and the fact that the length of the other diagonal is 6, we can finally find the area of our rhombus:
[tex] \dfrac{6 \cdot 8}{2} = \boxed{24} [/tex]
The area of the rhombus is 24 units^2.
