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John was visiting four cities that form a rectangle on a coordinate grid at A(0, 4), B(4, 2), C(1, -4) and D(-3, -2). What is the area of the space that cities enclose? Round your answer to the nearest whole number. Do not include units in your answer.

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Answer:


Area = 30

Explanation:

Given

Rectangle coordinates


A = (0,4)


B = (4,2)


C = (1,-4)


D =(-3,-2)

Required

The area of the rectangle

The area is calculated as:


Area = Length* Width

The length of the rectangle will be represented as:


Length = AB = CD

And the width is:


Width = BC = AD

Calculate distance AB using:


AB = √((x_1 - x_2)^2 +(y_1 - y_2)^2 )

Where:


A = (0,4) ---
(x_1,y_1)


B = (4,2)
--- (x_2,y_2)


AB = √((0 - 4)^2 +(4 - 2)^2 )


AB = √((- 4)^2 +(2)^2 )


AB = √(16 +4 )


AB = √(20)

Calculate distance BC using:


BC = √((x_1 - x_2)^2 +(y_1 - y_2)^2 )


C = (1,-4)
---(x_1,y_1)


B = (4,2)
--- (x_2,y_2)


BC = √((1 - 4)^2 +(-4 - 2)^2 )


BC = √((- 3)^2 +(-6)^2 )


BC = √(9 +36)


BC = √(45)

So, the area is:


Area = Length * Width


Area = AB * BC


Area = √(20) * √(45)


Area = √(20 * 45)


Area = \sqrt{900


Area = 30

User Expedito
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