Answer:
Area of the rhombus is a is a repeating decimal or a rational number.
Step-by-step explanation:
The area of a rhombus can be evaluated using the formula
![Area=\frac{1}{2}d_1d_2](https://tex.z-dn.net/?f=Area%3D%5Cfrac%7B1%7D%7B2%7Dd_1d_2)
where, d1 represents the measure of one of its diagonals and d2 represents the measure of its other diagonal.
Repeating decimal: After decimal the same sequence of digits repeats indefinitely. For example 2.333.. and 5.666.. etc.
Terminating decimal: It is a decimal number with a finite number of digits after the decimal. For example: 2.34 and 6.872 etc.
Rational numbers: A number which can be defined as p/q , where p and q are integers and q≠0, then the number is called a rational number.
Repeating decimal and Terminating decimal are rational numbers.
Product of two or more rational numbers is a rational number.
Product of a repeating decimal and terminating decimal is always a repeating decimal.
Let
and ![d_2=\frac{11}{4}=2.75](https://tex.z-dn.net/?f=d_2%3D%5Cfrac%7B11%7D%7B4%7D%3D2.75)
![Area=\frac{1}{2}(\frac{7}{3})(\frac{11}{4})](https://tex.z-dn.net/?f=Area%3D%5Cfrac%7B1%7D%7B2%7D%28%5Cfrac%7B7%7D%7B3%7D%29%28%5Cfrac%7B11%7D%7B4%7D%29)
![Area=\frac{77}{24}](https://tex.z-dn.net/?f=Area%3D%5Cfrac%7B77%7D%7B24%7D)
![Area=3.20833333333](https://tex.z-dn.net/?f=Area%3D3.20833333333)
Therefore, the area of the rhombus is a is a repeating decimal or a rational number.