Question

Find the area of rectangle ABCD with vertices A(-3,0)B(3,2C(4,-1)D(-2,-3)

Answer 1

The area of the triangle is 20. 

You can find this by plotting each of the points and drawing the triangle. You can then use the distance formula to determine each side length. The triangle will be $\sqrt{40}$ on one side and $\sqrt{10}$ on the other. When multiplied together, it will give you the above answer. 

Answer 2

Area of rectangle ABCD is 20

What is area of rectangle?

The area of the space occupied within the perimeter of a rectangle is called the area of a rectangle. It is calculated by finding the product of the length and breadth of the rectangle.

area of rectangle = Length * Breath

What is Distance formula?

The distance between two points using the given coordinates can be calculated by applying the distance formula.

Formula for Distance Between Two Points:

The formula for the distance, d, between two points whose coordinates are (x1,y1) and (x2,y2) is:

d = $\sqrt{[x_{2}-x_{1} ]^{2} + {[y_{2}-y_{1}]^{2} }$

This is called the Distance Formula.

According to question

Length of rectangle = AB

Breath of rectangle = BC

AB = $\sqrt{[3-(-3) ]^{2} + {[2- 0]^{2} }$

AB = $\sqrt{[6) ]^{2} + {[2]^{2} }$

AB = $\sqrt{40 }$

BC = $\sqrt{[4-(3) ]^{2} + {[-1 -(-2)]^{2} }$

BC=$\sqrt{[1 ]^{2} + {[-3]^{2} }$

BC=$\sqrt{10 }$

Area of rectangle = Length * Breath

= $\sqrt{40} * \sqrt{10}$

= $\sqrt{400}$

= 20

Hence , Area of rectangle ABCD is 20 .

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