Answer:
7.5 sq units
Step-by-step explanation:
Let's list out all the points in the triangle.
(0,4) (4,1) and (5,4)
Find the distance b/w each side
distance b/w (0,4) and (4,1) is
[tex]\sqrt{(1-4)^{2}+( 4-0)^{2} }[/tex] =[tex]\sqrt{(-3)^{2}+16 } =\sqrt{9+16}=\sqrt{25} =5[/tex]
distance b/w (4,1) and (5,4) is
[tex]\sqrt{(4-1)^{2}+(5-4)^{2} }=\sqrt{9+1}=\sqrt{ 10 }[/tex]
distance b/w (5,4) and (0,4) is
[tex]\sqrt{(4-4)^2+(0-5)^2}=\sqrt{25} =5[/tex]
So the given triangle is an isoscles triangle meaning 2 sides are equal.
So we can use the formula 1/2*base*height=
1/2*[tex]\sqrt{10}[/tex]*5
=0.5*3.16*5=7.905
So the approximate answer would be 7.5 sq units
