Mathematics
Grade6
Easy

Question

Calculate the area of rectangle ABCD.

  1. 10 sq. units    
  2. 14 sq. units    
  3. 12 sq. units    
  4. 8 sq. units    

Hint:

Rectangle ABCD is plotted on a x-y graph. We are given the coordinates of the points. We are asked to find the area of the rectangle. Area is the plane enclosed by the border of shape. We will do this by finding the absolute distance of two adjacent sides. And then find the area using the formula of area for rectangle.

The correct answer is: 10 sq. units


    The coordinates of the rectangle ABCD are
    A is (-3,4)
    B is (2,4)
    C is (2,2)
    D is (-3,2)
    We have to find the length of the adjacent sides.
    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) As 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
    We will find the length of side AB.
    For the points A and B, y coordinate is same. We will find the absolute distance using x coordinate.
    Absolute distance of the point A = |-3|
    Absolute distance of the point B = |2|
    Length of AB = |-3| + |2|
    = 3 + 2
    = 5
    Length of the rectangle is 5 units.
    We will find the length of side BC.
    For the points B and C, x coordinate is same. We will find the absolute distance using x coordinate.
    Absolute distance of the point B = |4|
    Absolute distance of the point C = |2|
    Length of BC = |4| - |2|
    = 4 - 2
    = 2
    Breadth of the rectangle is 2 units.
    The formula for perimeter is (length × breadth)
    Perimeter of the rectangle ABCD = (length × breadth)
    = (5 × 2)
    = 10 sq. units
    Therefore, perimeter of the rectangle is 10 sq. units.

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

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