Question
Calculate the area of the rectangle whose coordinates are A (10, 10), B (10, 26), C (45, 26), D (45, 10)
- 560 sq. units
- 102 sq. units
- 56 sq. units
- 260 sq. units
Hint:
A rectangle ABCD is plotted on the graph. 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: 560 sq. units
The given coordinates of the rectangle are:
A is (10,10)
B is (10,26)
C is (45,26)
D is (45,10)
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.
We will consider the side AB as length and BC as breadth.
A and B have same signs so they are in same quadrant. And points B and C have same signs so they are in same quadrant.
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 = |10|
Absolute distance of the point B = |26|
Length of AB = |26| – |10|
= 26 – 10
= 16
Length of the rectangle is 16 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 = |10|
Absolute distance of the point C = |45|
Length of BC = |45| - |10|
= 35
= 35
Breadth of the rectangle is 35 units.
The formula for area is length × breath
Area of rectangle ABCD = length × breadth
= 16 × 35
= 560 sq. units.
Therefore, area of the rectangle is 560 sq. units.
A is (10,10)
B is (10,26)
C is (45,26)
D is (45,10)
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.
We will consider the side AB as length and BC as breadth.
A and B have same signs so they are in same quadrant. And points B and C have same signs so they are in same quadrant.
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 = |10|
Absolute distance of the point B = |26|
Length of AB = |26| – |10|
= 26 – 10
= 16
Length of the rectangle is 16 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 = |10|
Absolute distance of the point C = |45|
Length of BC = |45| - |10|
= 35
= 35
Breadth of the rectangle is 35 units.
The formula for area is length × breath
Area of rectangle ABCD = length × breadth
= 16 × 35
= 560 sq. units.
Therefore, area of the rectangle is 560 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.
