Let us understand the derivation of this formula with the help of the following figure, where 'd' is the diagonal and 's' represents the sides of the square. Here the side of the square is 's' and the diagonal of the square is 'd'. Now, this formula will help us to find the area of the square, using the diagonal.
In the above section, we covered the definition of area of square as well as area of square formula. In this section let us understand how to use the area of the square formula to find its area with the help of few applications or real-world examples. Example: Find the area of a square park whose perimeter is ft.
Example: Find the area of a square park whose side is 90 ft. Example: Find the area of a square park whose diagonal is 14 feet. A common mistake that we tend to make while calculating the area of a square is doubling the number. This is incorrect! Example 1: What is the area of a square-shaped swimming pool whose one side is equal to 8 m? Therefore, the area of the swimming pool is 64 square meters. Example 2: The area of a square-shaped carrom board is cm 2.
What is the length of its side? Therefore, the side of the carrom board is 60 cm. Example 3: Find the area of the square-shaped floor room which is made up of square tiles of side 15 inches. We know that there are tiles on the floor of the room. Therefore, the area of the floor is square inches. Therefore, the area of the carpet is 8 square feet. In geometry, the square is a shape with four equal sides.
The area of a square is defined as the number of square units that make a complete square. Since the area of a square is a two-dimensional quantity, it is always expressed in square units. Check now area of square calculator for quick calculations. What could the area of this shape be?
There is more than one possible answer to this question. One way of working out a possible answer would be to draw a rectangle and then work out what the sides could be if the perimeter is 36cm. This will probably involve a lot of trial and error. A child may finally arrive at the measurements: 10cm and 8cm. More like this.
Area explained. What is the perimeter? Calculate and measure areas. If you dislike it you can choose another one. Area is about the number of units that can fit into the space. If you have a square with a length sides. You can break that square into a grid of size 1 unit for each block in the grid 1:a on both axes. If you count the number of units, that is the blocks in the grid, you've calculated the area.
A square of unit width and length of 1 , has only one unit grid contained and thus the area is 1. Imagine a rectangle in 2-d space. If you make a copy of that rectangle and rotate it degrees around the one of the sides through the third dimension, you will have two copies of the rectangle in that 2-d space. They share a side and so there is no overlap or gap between them.
The tops and bottoms of the rectangles will form a straight line because the corners are right angles. The result is a larger rectangle that could be 'copied' again in the same way along any of its sides. Or you copy just one of the rectangles. You could copy the original rectangle as many times as you want in the x direction and then as many times as you want in the y direction and end up with one large rectangle whose area is a multiple of the original rectangle, since there is no overlap or gaps.
Suppose the original area of the rectangle is A, and you've chosen to copy the rectangle so that there are x total copies in one direction and then y total copies of the result in a perpendicular direction.
You will end up with a rectangle that first has area Ax, and then Axy. This should hold in the general sense that for whatever value of x and y you chose, the area will be Axy.
Now suppose the original rectangle is a square, and that both x and y values are the same x so that the larger square remains a square.
If the original square has a side length of 1, then is it always true that the area of the original square is 1? You can construct a square with side length 2 by choosing x and y as 2 and 2. This is built out of 4 copies of the original square so the area must be 4 times as great. You must then make a decision at the start. Either all rectangles have 0 area or the unit square has area 1. Sign up to join this community.
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Learn more. Why is the area of a square equal to side squared?
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