**Perimeter And Area Of Rectangle**

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**How To Find The Perimeter of a Rectangle**

The perimeter of a rectangle can be defined as the distance round any given rectangular shape. Recall that a rectangle is a polygon with 4 sides. Talking about the properties of a rectangle, note well that all the angles of a rectangle are 90º and also, the opposite sides of a rectangle are equal to each others.

Thus, one can say that the perimeter of a rectangle defines the the total length of all the sides of the rectangle. When we add the values of all the 4 sides of any rectangle together, the answer we get is the perimeter of the rectangle.

The formula for the perimeter of a rectangle can be derived as follows:

Let a be the length of a rectangle and b the width of the rectangle. A rectangle has two lengths and two widths each of which are equal to each other. Put in a better way, the opposite sides of a rectangular figure are equal at all times.

Thus, Perimeter Of A Rectangle = a + a + b + b

Perimeter Of A Rectangle = 2a + 2b

Therefore, formula to find the Perimeter Of A Rectangle = 2(a + b) units

From the above derivations, we cam deduce that the length and width dimensions of a rectangle must be known before the perimeter can be calculated. So we can say that the perimeter of any given rectangle with length ‘a units’ and width ‘b units’ can be calculated as:

a + b + a + b = 2a + 2b = 2 (a + b) units.

In simple terms, the formula for computing the perimeter of a rectangle is = 2 × (the sum of the 4 adjacent sides of the rectangle)

**Perimeter Of A Rectangle Calculator**

**Question One:** The two sides of the rectangle are given as 21 cm and 13 cm. Calculate the perimeter of the rectangle.

**Answer:** Perimeter Of A Rectangle Formula = 2(a + b) Units. That is 2 times the sum of adjacent sides.

Side A = 21 cm

Side B = 13 cm

Substituting these values into the Perimeter Of A Rectangle Formula, we have as follows:

2(a + b) = 2 × (21 + 13) = 2 × (34) = 68 cm

Thus, the Perimeter Of the Rectangle is 68 cm

**Question Two:** The dimensions of a nursery school rectangular field are 45 m length and 19 m breadth. Using this information, calculate the perimeter of the nursery school rectangular field.

**Answer:** Perimeter Of A Rectangle Formula = 2(a + b)

Let the length of the school’s rectangular field be known as “a” while the breadth be known as “b” so that we can have:

a = 45 m

b = 19 m

But the perimeter of a rectangle formula is = 2 × (sum of adjacent sides)

Therefore, we substitute the given information into the above formula as follows:

2 (a + b)

= 2 × (45 + 19)

= 2 × (64)

= 132 m

Therefore, the perimeter of the school’s rectangular field is equal to 132 m.

Now, there can be twisted questions regarding the perimeter of a rectangle where the value of one side of the rectangle is given alongside the perimeter and you are requested to find the value of the other side.

**First Example:** The length of one side of a rectangle is given as 63 cm while the perimeter of the same rectangle is calculated to be 300 cm. Determine the measurement of the other side of the rectangle.

**Solution Of The Question:** Formula for finding the Perimeter Of A Rectangle = 2 (a + b) units

From the question above, the perimeter of the rectangle is given as 300 cm while the length (a) is given as 63 cm. To find the value of the width (b) which is the missing side, we will substitute into the formula as follows:

Perimeter Of A Rectangle = 2 x (a +b)

300 cm = 2 (63 cm + b)

300 = (2 x 63) + (2 x b)

300 = 126 + 2b

2b = 300 – 126

2b = 174

b = 174 ÷2

Therefore b = 87

Thus, the width of the rectangle is 87 cm which can be proved as follows.

Perimeter Of A Rectangle = 2 x (a +b)

300 = 2 (63 + 87)

300 = 126 + 174

300 = 300

**Finding Sides Using The Properties Of A Rectangle**

**Second Example:** We can also be asked to find the other sides of a rectangle when given the value of just 2 sides. – Perimeter And Area Of Rectangle

For instance, there is a rectangle with 4 sides a, b, c and d. The value of side a is 7 cm while the value of side b is given as 2.5 cm. Note that side a and side c are adjacent to each other while side b and side d are also adjacent to each other. Find the values of side c and side d using the following information presented above.

**Answer:** The formula for the Perimeter of a rectangle is = 2 x (a + b) units. That is 2 (sum of the adjacent sides or sides facing each other directly).

From the equation, we understand that a and b are sides adjacent to the remaining two sides of the rectangle noted as side c and side d.

From the question, side a = 7 cm while side b = 2.5 cm.

To find side c and d, we should recall that property of a rectangle which asserts that the sizes of the opposite sides of a rectangle are always equal.

Hence, side a is equal to side c. Thus side c is equal to 7 cm. On the other hand, side b is equal to side d. Thus side d is equal to 2.5 cm.

**How To Find Area And Perimeter Of A Rectangle**

Below are the methods of How to find the perimeter and area of a rectangle.

The area of rectangle formula is given as :

Area Of Rectangle = Length x Width

On the other hand, the perimeter of a rectangle formula is given as:

Perimeter Of Rectangle = 2 (Sum Of The Adjacent Sides Of The Rectangle) Units

**Example:** What are the perimeter and area of rectangle abcd where length a is 5 cm, width b is 4 cm? What are the perimeter and area of this rectangle?

**Solution:** How to do area and perimeter of a rectangle is to apply the formulas as follows:

Area Of A Rectangle Formula = Length x Width

Thus, Area Of A Rectangle = 5 x 4

Area Of A Rectangle = 4 cm²

Perimeter Of A Rectangle Formula = 2 (a + b) units

Perimeter Of A Rectangle = 2 (5 x 4)

Perimeter Of A Rectangle = 2 x 20

Therefore, Perimeter Of Rectangle = 40 cm

**What Is The Area And Perimeter Of A Rectangle**

The Area Of A Rectangle can be defined as the total region or space covered by the 4 sides of any given plain rectangular figure. The formula for finding Area Of A Rectangle is given as follows:

Area Of A Rectangle Formula = Length x Width

The Perimeter Of A Rectangle can be defined as the distance round any given rectangular shape. It is calculated by adding together the values of the 4 sides of any given rectangle. Thus, the formula for perimeter of a rectangle is given as:

Perimeter Of Rectangle = 2 (a + b) Units (that is 2 time the sum of the adjacent sides of a rectangle)

**How To Find The Length And Width Of A Rectangle When Given The Perimeter And Area**

Perimeter And Area Of Rectangle – This section is all about How to find the dimensions of a rectangle given the perimeter and area. We will show you how to find the length and width of a rectangle when given the perimeter and area.

Remember that the area of a rectangle is the total region covered by its four side on a plain surface while the perimeter of a rectangle can be defined as a measurement of the total distance round a rectangle determined by summing its 4 sides together.

**Example:** If the perimeter of a rectangle is 200 meters and the area of the rectangle is as large as possible, calculated the length and width dimensions of the rectangle. – Perimeter And Area Of Rectangle

**Solution:**

Area of a rectangle formula = length × width

Perimeter of a rectangle formula = 2 (length + width)

Let ‘A’ stand for the area of the rectangle and ‘P’ represent the perimeter of the rectangle.

Also, let ‘a’ be the length of the rectangle and ‘b’ be the width of the rectangle.

Perimeter of rectangle = 2 (length + width)

Thus, P = 2 (a + b)

200 = 2 (a + b) (Since the Perimeter of the rectangle is 200 meters)

Dividing each side of the equation by 2, we have:

200 ÷ 2 = 2 (a + b) ÷ 2

Thus a + b = 100

Therefore b = 100 – a ————— (Equation 1)

Recall that the Area of a rectangle = Length × Width

Thus, A = a b ————— (Equation 2)

When we substitute equation 1 into equation 2, we have the following:

A = a (100 – a)

Area A(a) = 100 a – a²

Computing the derivative of A(a) we have,

A'(a) = 100 – 2 a

Finding the critical points,

100 – 2 a = 0

2 a = 100

Therefore, a = 50

To get the value of b, we substitute a = 50 into equation (1) as follows:

b = 100 – a

b = 100 – 50

Therefore, b = 50

Perimeter And Area Of Rectangle – Hence, the rectangle with maximum area is a square shape with side lengths of 50 meters. Thus, the dimensions of the rectangle which has a perimeter of 200 meters and a maximum area are 50 meters long and 25 meters wide.

**If a rectangle has a perimeter of 36 feet, and it is 4-feet wide, what is its area?**

Perimeter Of A Rectangle = 2 (a + b)

Let “a” be length and “b” be width

Therefore we have as follows:

36 = 2 (a + 4)

36 = 2 a + 8

2 a = 36 – 8

2 a = 28

a = 28 ÷ 2

Therefore Length “a” = 14 ft

But Area Of A Rectangle = Length x Width

Length of Rectangle = 14 ft

Width Of Rectangle = 4 ft

Area Of A Rectangle = 14 x 4

Therefore, Area Of The Rectangle = 56 ft²

**The perimeter of a rectangle in which the height is 8 inches and the area is 28*in^2**

Area Of A Rectangle = Length x Width

28 = 8 x Width

Width = 28 ÷ 8

Therefore, Width of the rectangle = 3.5 inches

Perimeter Of Rectangle = 2 (a + b) units

Perimeter Of Rectangle = 2 (8 + 3.5)

Perimeter Of Rectangle = 2 x 11.5

Therefore, Perimeter Of The Rectangle = 23 inch²

**Work At Home:**

- Find the dimensions of a rectangle whose perimeter is 22 meters and whose area is 24 square meters.
- Find the dimensions of a rectangle whose perimeter is 22 meters and whose area is 28 square meters.
- Find the dimensions of a rectangle whose perimeter is 18 meters and whose area is 20 square meters.
- Length and width of rectangle with perimeter 76 that has the maximum area, what is the maximum area?
- If the perimeter of a rectangle is 48 and the area is 135 what is the width and length?

I hope you have really leant a lot about this topic today. See you again in our next lesson dropping soon. Feel free to read **Powerful Prayer Points** to enhance your spiritual life. You can also **Download Latest DJ Mixtapes**. Learn more about **How To Find The Area Of A Rectangle**. Cheers!