Find the area and perimeter of the rectangle with vertices (5 , -7) (5 ,1) (-2 ,1) and (-2, -7).
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(-2,1) *""""""""""1|""""""""""""""""""""""""""* (5,1)
__________________|_______0_________________|________
-7 -6 -5 -4 -3 -2 -1 -1| 1 2 3 4 5 6 7
| -2| |
| -3| |
| -4| |
| -5| |
| -6| |
(-2,-7) *"""""""" -7|"""""""""""""""""""""""""""* (5,-7)
On the coordinate plane I made, the rectangle which looks sort of like a square has a length(top and bottom) of 7 units, and a width(left and right side) of 8 units.
Perimeter of a Rectangle is 2l + 2w. The area is Length * Width.
The area of the Rectangle is 56 units, because 7 * 8 = 56.
The perimeter is 30 units, because 2 * 7 + 2 * 8 simplifies to 14 + 16, and that equals 30.
ouch don't pay attention to the coordinate plane, the typing box is inaccurate and doesn't really allow you to make a coordinate plane or something similar like you want it to, but the answer below is correct.
To find the area and perimeter of a rectangle, we need to use the formula:
Area = length × width
Perimeter = 2 × (length + width)
A rectangle is a quadrilateral with opposite sides parallel and equal in length. In this case, we can determine the length and width by finding the distance between the given vertices.
For the length:
The first and second vertices (5, -7) and (5, 1) have the same x-coordinate, so they lie on the same vertical line. The distance between them is the absolute difference between their y-coordinates:
Length = | -7 - 1 | = 6 units
For the width:
The second and third vertices (5, 1) and (-2, 1) have the same y-coordinate, so they lie on the same horizontal line. The distance between them is the absolute difference between their x-coordinates:
Width = | 5 - (-2) | = 7 units
Now that we have the length and width, we can calculate the area and perimeter.
Area = length × width = 6 units × 7 units = 42 square units
Perimeter = 2 × (length + width) = 2 × (6 units + 7 units) = 2 × 13 units = 26 units
Therefore, the area of the rectangle is 42 square units and its perimeter is 26 units.
If you plot the points, you will see that the sides are vertical and horizontal lines.
Thus all you have to do is "count" what the length and width of the rectangle is.