Mathematics
Grade6
Easy

Question

Calculate the area of the rectangle whose coordinates are as follows

  1. 100    
  2. 450    
  3. 110    
  4. 480    

Hint:

We are given the coordinates of the corner of a rectangle ABDC. We are asked to find the area of the rectangle. Area means the plane enclosed by the border of the shape. To solve this question, we will find any two adjacent sides. Once we find the adjacent sides, we will use the formula for perimeter of a rectangle.

The correct answer is: 450


    The given coordinates of the rectangle are:
    A is (-20,20)
    B is (-20,30)
    C is (25,30)
    D is (25,20)
    We have to find the length of the adjacent sides of rectangle ABCD
    To find the length we will use the following criteria:
    1) If x coordinate is same, we will find the absolute distance using y coordinate. An absolute distance is the length of the point from the respective axis. If x coordinate is same then its length is measured from x axis. It is a positive quantity.
    2) If y coordinate is same we will use the x coordinate to find absolute distance.
    3) If the points are in same quadrant, we will have to subtract the absolute distances to find length.
    4) If the points are in adjacent quadrants, we will have to add the absolute distances to find length.
    We will consider the side AB as length and BC as breadth.
    From the figure, we can see points A and B are in same quadrant. Similarly, B and C are in adjacent quadrants.
    We will find the length of side AB.
    For the points A and B, x coordinate is same. We will find the absolute distance using y coordinate. It is distance from x axis.
    Absolute distance of the point A = |20|
    Absolute distance of the point B = |30|
    Length of AB = |30| - |20|
    = 30 - 20
    = 10
    Length of the rectangle is 10 units.
    We will find the length of side BC
    For the points B and C, y coordinate is same. We will find the absolute distance using x coordinate. It is distance from y axis.
    Absolute distance of the point B = |-25|
    Absolute distance of the point C = |20|
    Length of BC = |-25| + |20|
    = 25 + 20
    = 45
    Breadth of the rectangle is 45 units.
    The formula for area of rectangle is (length × breadth)
    Area of rectangle ABCD = (length × breadth)
    = (10 × 45)
    = 450 sq. units
    Therefore, area of the rectangle is 450 sq. units.



    For such questions, we have to see if the points of the rectangle are in same quadrant or adjacent quadrants. We can use distance formula to find the length of sides of rectangle too.

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