Answer:
Because the irrational number can not be expressed as the ratio of two integers and it is not an imaginary number.
Step-by-step explanation:
Given
The length of one base of trapezoid = 3.6cm =
The length of other base of trapezoid =[tex]12\frac{1}{3}[/tex]=[tex]\frac{37}{3}[/tex]
The height of trapezoid= [tex]\sqrt{5}[/tex] cm
By using formula of area of trapezoid, a=[tex]\frac{1}{2} (b_1+b_2)\times h[/tex]
Substitute the value of [tex]b_1, b_2[/tex] and h in the formula of area of trapezoid
Area of trapezoid=[tex]\frac{1}{2} (\frac{36}{10} +\frac{37}{3} )\times \sqrt{5}[/tex]
Area of trapezoid=[tex]\frac{1}{2} (\frac{108+370}{30}) \times \sqrt{5}[/tex]
Area of trapezoid=[tex]\frac{1}{2} \times \frac{478}{30} \times\sqrt{5}[/tex]
Area of trapezoid=[tex]\frac{239}{30} \sqrt{5}[/tex] [tex]cm^2[/tex]
Let a and b are two integers and let area of trapezoid is rational number
Therefore, the rational number can be write in the ratio of two integers a and b
[tex]\therefore \frac{239}{30} \sqrt{5}=\frac{a}{b}[/tex] where [tex]b \neq 0[/tex]
[tex]\frac{30a}{239b} =\sqrt{5}[/tex]
We know that [tex]\sqrt{5}[/tex] is a irrational number and [tex]\frac{30a}{239b}[/tex] is a rational number
Irrational number can never be equal to rational number
Therefore, the area of trapezoid is irrational number.
