Mathematics
Grade6
Easy
Question
Calculate the area of the rectangle whose coordinates are A (-45, -16), B (-45, -5), C (-8, -5), D (-8, -16)
- 96 sq. units
- 120 sq. units
- 407 sq. units
- 128 sq. units
Hint:
We are given the coordinates of the corners of the rectangle. 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: 407 sq. units
The coordinates of the rectangle ABCD are
A is (-45,-16)
B is (-45,-5)
C is (-8,-5)
D is (-8,-16)
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) 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
The points A,B,C and D have same signs of coordinates. So, they are in same quadrant.
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, 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 = |-16|
Absolute distance of the point B = |-5|
Length of AB = |-16| - |-5|
= 16 – 5
= 11
Length of the rectangle is 11 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 = |-45|
Absolute distance of the point C = |-8|
Length of BC = |45| - |-8|
= 45 – 8
= 37
Breadth of the rectangle is 36 units.
The formula for area is (length × breadth)
Area of rectangle ABCD = (length × breadth)
= (11 × 37)
= 407 sq. units
Therefore, area of the rectangle is 407 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 adjacent quadrants, we have to add the absolute values. We can use distance formula to find the length of sides of rectangle too.
