Final answer:
To find the area or perimeter on a coordinate plane, I break the shape into simpler parts or use the properties of regular shapes. Subtract coordinates to find dimensions, multiply for area, and sum lengths for the perimeter. Comparing areas involves ratios, using the side² formula for squares.
Step-by-step explanation:
Finding the Area or Perimeter of Shapes on a Coordinate Plane
When it comes to finding the area or perimeter of shapes on a coordinate plane, I prefer using methods that offer clarity and simplicity. My preferred method involves breaking down the shape into known geometrical figures, such as rectangles and triangles, and then calculating the area of each individual part before summing them up. For the perimeter, I like to use the distance formula to find the lengths of each side if the shape is irregular. For regular shapes like rectangles, it is simple: multiply two adjacent sides to get the area and add all sides' lengths to get the perimeter.
Let's consider the calculation of a rectangle on a coordinate plane. If we have the coordinates of the opposite corners (let's say A and B), the length and the width of the rectangle can be easily found by subtracting the x-coordinates to find the width, and the y-coordinates to find the length. Then we calculate the area by multiplying the length by the width. The perimeter is found by adding twice the length and twice the width. As an example, if A is at (2,3) and B is at (5,6), then the width is 5-2=3 and the length is 6-3=3. Therefore, the area is 3*3=9 units squared and the perimeter is 2*(3+3)=12 units.
If dealing with a circle, remember that the area is πr² and the circumference is 2πr. With a radius of 3 meters, our area would be π*3²=π*9 square meters and the circumference would be 2*π*3=6π meters.
Comparing Areas
To compare the area of two squares of different sizes, we can write a ratio of their areas. Since the area of a square is given by side², if one square's side is twice as long as the other's, its area will be four times greater. By using this method, we can compare areas efficiently without needing to memorize numerous formulas, as understanding the properties of shapes is more beneficial and adaptable.