Answer:
30
Step-by-step explanation:
units from (-1,1) to (5,-1) and (-1,-4) to (5,-4) = 6 units
units from (-1,1) to (-1,-4) and (5,-1) to (5,-4) = 5 units
area of rectangle = L X b
= 6 X 5
= 30
Area of the given rectangle is 30 square unit.
The area occupied by a rectangle within the boundary of the rectangle is called the area of the rectangle.
Now, if the length of the rectangle be "l" and the width be "w" then,
Area of rectangle = l × w
Vertices of the given rectangle are (-1 , 1) , (-1 , -4 ) , (5, -4 ) and (5 , 1)
The distance between (5, -4 ) & (-1 , -4 ) is the length of the rectangle.
By the distance formula distance between (5, -4 ) & (-1 , -4 )
[tex]=\sqrt{(5-(-1))^{2}+((-4)-(-4))^{2} }[/tex]
[tex]=\sqrt{(5+1)^{2} +(-4+4)^{2} }[/tex]
[tex]=\sqrt{(6)^{2}+0 }[/tex]
[tex]=\sqrt{36}[/tex]
[tex]=6[/tex] (∵ we neglect the negative value)
So the length of the rectangle is 6 unit.
The distance between (5 , 1) & (5, -4 ) is the width of the rectangle.
By the distance formula distance between (5 , 1) & (5, -4 )
[tex]=\sqrt{(5-5)^{2} +(1-(-4))^{2} }[/tex]
[tex]=\sqrt{0+(1+4)^{2} }[/tex]
[tex]=\sqrt{(5)^{2} }[/tex]
[tex]=\sqrt{25}[/tex]
[tex]=5[/tex] (∵ we neglect the negative value)
So the width of the rectangle is 5 unit.
∴ Area of a rectangle = l × w
= (6×5) square unit
= 30 square unit
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