The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all the four sides. x is in this case the length of the rectangle while y is the width of the rectangle. Show
The perimeter, P, is: $$P= x+x+y+y$$ $$P=2x+2y$$ $$P=2(x+y)$$  Example Find the perimeter of this rectangle: $$P=7+7+4+4$$ $$P=2\cdot 7+2\cdot 4$$ $$P=2\cdot (7+4)$$ $$P=2\cdot 11$$ $$P=22\,in$$ The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y. $$A=x\cdot y$$ Example Find the area of this square. $$A=x\cdot y$$ $$A=5\cdot 5$$ $$A=25\,in^{2}$$ There are different units for perimeter and area The perimeter has the same units as the length of the sides of rectangle or square whereas the area's unit is squared. Video lessonCalculate the perimeter and the area in feet Have you observed the shapes around you? Everything in our surroundings has a shape. For example, have you seen a photo frame? Can you tell its shape just by looking at it? Well, it should not be difficult. Its shape can either be square, rectangle, circle, or oval. No matter the shape, they always have a boundary like that of the photo frame. If you were to wrap a sheet of paper around the periphery of the photo frame, you would get the perimeter of that shape. One can apply this logic in daily life also. For instance, if you were to walk around a square-shaped park, the area you would cover by walking around its boundary would be equal to the perimeter of the park. Knowing this, one can easily understand how much they walk while in the park. Keep reading to understand what a perimeter is. What is the perimeter of a shape?A shape has a particular boundary that encloses the complete structure when we look at a figure. Be it a box, a frame, a park, or a building. Every design is held within a limit known as the perimeter. When we talk about the perimeter of a shape, it is referred to the total length of its boundary. However, a perimeter is only a two-dimensional geometric shape. One can easily calculate the perimeter of a shape by knowing the length of each side of that particular shape. For example, if you want to draw the boundary of your book, which is rectangular, you would be able to do this by measuring each side and adding together. By adding the length of each side of the book, one can easily know the perimeter of the boundary of the book. What do you understand about the perimeter of a square?After knowing what the perimeter of a shape is, it will be easy to understand the perimeter of the square. The perimeter of a square is the area that covers the boundary of a square-shaped object. For example, if one rides a bicycle around a square-shaped park, to find out the area they covered will be equal to the perimeter of that particular park. Another example can be a square table. If a person wants to decorate the boundary of the square table with a ribbon, then the total length of the ribbon needed by them will be equal to the perimeter of the table. The frame of a square is the total sum of the lengths of its four sides. The perimeter of a square: FormulaThe perimeter of a square is calculated as the sum of the lengths of its four sides. Since all sides of a square are equal, one can multiply one side four times to calculate its perimeter. If a square has a side of length A, the perimeter will be four times A. The perimeter of square= 4 × A Therefore, The perimeter of square= 4 × Side What are the advantages of knowing the perimeter of the square?There are various advantages of knowing the perimeter of not only a square but also of other shapes. By knowing the perimeter of a shape, or in this case of a square, one can also calculate the length of each side. It means that if the perimeter of a square shape is 12 cm, one can easily calculate the side by dividing it by 4. For example, Perimeter= 12 cm Length of one side= X Perimeter= 4 × X 12 = 4 × X X = 12/4 X = 3 cm Apart from this, one advantage of knowing the perimeter of a square is that you can also calculate the area of a square. From the above calculation, it is clear that one can calculate the unknown side of a square if the perimeter is known. And if one side is known, it will be easy to calculate the area, i.e., side × side. The perimeter of square: Derivation The perimeter of a square is the area that covers the total length of the boundary of that square. One can easily define the perimeter of a square as a border that encloses a space inside it. To find out the perimeter of a Polygon, one can do it by a simple formula. Perimeter = sum of all the sides of a polygon Therefore, The perimeter of a square = sum of all the sides of the square Perimeter of a square = side + side + side + side (a square has four sides) The perimeter of a square = 4 × side How to find out the perimeter of a square?From the above derivation, it is clear that the sum of lengths of all the sides of a square gives the perimeter of the square. It would be important to note that even if one side of a square is known and the rest of the three sides are unknown, it is still possible to calculate the perimeter of the square. It is because a square has four sides that are equal in length. So, by knowing the length of just one side, it is possible to calculate the perimeter of the whole square. For example, if one side of a square is 16 cm, then its perimeter will be- Perimeter of a square = 4 × side Perimeter of a square = 4 × 16 The perimeter = 64 cm How to use diagonal to calculate the perimeter of a square?A square is a Polygon that has all sides equal in mathematical terms. It means each side of a square makes a right angle (90°) at their point of intersection. This information can help one calculate the perimeter of a square. When there is a diagonal in a square, it divides the square into two halves. These halves become two right-angled triangles. Thus, sharing all the properties of a right-angle triangle. In this case, the diagonal becomes the hypotenuse. So, by Pythagoras theorem, one can use the hypotenuse to calculate the side of a square. Thus, Diagonal = hypotenuse Side = Diagonal/√2 How to calculate the perimeter of a square by its area?An area of a square is referred to the area enclosed within its perimeter. In other terms, an area is a space occupied by a Polygon. Talking about the area of a square, one can calculate it by multiplying one side with its other side. However, because each side is the same length, one can calculate its area by squaring one of its sides. For example, if one side of a square is 4 cm, then its area will be, Area of the square = side × side Or, Area of the square = (side)² = 4² = 16 cm² Now that it is easy to calculate the area of a square, it would be effortless to extract the perimeter when its area is given. Suppose the area of a square is 25 cm². And you are asked about calculating its perimeter. The steps are pretty simple.
Calculation: Area of the square = 25 cm² One side of the square = √area of square One side of the square = √25 Length of one side = 5 cm Now, if one side of the square of 5 cm, its perimeter will be, The perimeter of the square = 4 × side The perimeter of the square = 4 × 5 Perimeter = 20 cm Some solved questions dealing with the calculation of the perimeter of the squareSample 1: The perimeter of a square is 16 cm. What will be the length of each side? Calculation: The perimeter of the square is 16 cm. Let the side length be ‘x’ cm. The perimeter of a square = 4 × (side) 16=4×(x) x = 4 cm Sample 2: If the side “a” is = 2 cm in a square. What will be the lengths of b, c, and d? Calculation: Side “a” of the square is = 2 cm. We use the property of a square that explains that all the sides of a square are equal in length. Therefore, side a = side b = side c = side d = 2 cm ConclusionKnowing the perimeter of all the geometrical shapes is a convenient way to ease various calculations. In this case, calculating the perimeter of a square can help one simplify multiple mathematical concepts. The above explanation deals with the definition, analysis, derivation, and examples of the perimeter of a square. The properties of a square help to calculate the area, perimeter, and length of its sides. How do you calculate a perimeter?In order to find the perimeter, or distance around the rectangle, we need to add up all four side lengths. This can be done efficiently by simply adding the length and the width, and then multiplying this sum by two since there are two of each side length. Perimeter=(length+width)×2 is the formula for perimeter.
How do you get the perimeter of a square from the area?Perimeter of Square Using Area of Square. Step 1: Note down the area of square.. Step 2: Calculate the side length using the area. Side = √area.. Step 3: Multiply this obtained value of side length, (√area) by 4 and express the answer in units. Perimeter = (√area) × 4 = 4√area units.. What is the formula of square?Area of a square = Side × Side = S2
Algebraically, the area of a square can be found by squaring the number representing the measure of the side of the square. Now, let us use this formula to find the area of a square of side 7 cm. We know that the area of a square = Side × Side.
What is the perimeter of a 4 cm square?=4×4=16cm.
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How do you calculate the perimeter of a square
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