# How To Find The Area Of A Rectangle?

While learning geometry, you must have studied how to find the area of a rectangle. We can find rectangle shapes everywhere in our daily life such as notebooks, tiles, blackboards, dining tables, TV, and more. The mathematical terms and concepts are vast! In today’s post, I will focus on how to find the area and perimeter of a rectangle. Here, we’ll see the formula of the area of a rectangle to determine areas of different rectangular surfaces. The term “area” is defined as the space covered by any closed figure. You can keep on reading to know more about how to find the area of a rectangle in detail.

## How To Find The Area Of A Rectangle?

In this section, I will teach you how to find the area of a rectangle. The area of any rectangular surface can be calculated by using the area of rectangle formula which is:

Area = Length x width OR Length x Breadth

Follow these steps to know how to find the surface area of a rectangle.

1. First, determine the length of the rectangle using a ruler.
2. Now, determine the width (breadth) of the rectangle using a ruler.
3. Then, multiply the values of the length and width of the rectangle by each other.
4. You’ll obtain the rectangle’s area by multiplying its length and breadth.

Thus, you can write your final answer in either cm. sq. or cm2

You can now keep on reading to know how to find the area of a rectangle without the width.

## Find The Area Of A Rectangle Using Pythagorean Theorem

When a diagonal is cut through the rectangle, it is divided into two right-angled triangles. In this case, we can use the Pythagorean theorem to find out the area of a rectangle.

Follow these steps to know how to find the area of a rectangle using the Pythagorean theorem.

1. First, determine the length of the rectangle using a ruler.
2. Now, determine the diagonal of the rectangle using a ruler.
3. Recall the formula of the Pythagorean theorem which is: c2 = a2 + b2.
4. Here, “c” is diagonal, “a” is length, and “b” is width.
5. Substitute the values of length and diagonal in this formula to find the value of width.
6. While solving this c2 = a2 + b2 equation, you’ll get the value of width.
7. Once you find the value of the width, substitute it in the area of the rectangle formula.
8. Here, multiple the length and width of the rectangle to get its area.

While using the Pythagorean theorem, you must recall all the square roots of different numbers.

## Find The Area Of A 3D Rectangle

There is a different formula when it comes to the area of a 3D rectangle object. For instance, consider a rectangular prism. Follow these steps to know how to find the area of a 3D rectangle.

1. First, determine the length of the rectangle using a ruler.
2. Now, determine the width (breadth) of the rectangle using a ruler.
3. Next, determine the height of the rectangle using a ruler.
4. Recall the formula of the area of a rectangular prism which is:

A = 2(width x length) + 2(length x height) + 2(height x width)

1. Substitute the values of the length, width, and height of the 3D rectangle.
2. Then, multiply and add the values of length, width, and height to get the area of a 3D rectangle.

You can even first add (wl + lh + hw) and then multiply the obtained value with 2. Both the area of 3D rectangle formulas will give you the same value.

Keep on reading to know the alternative ways to learn how to find the area of a rectangle.

## Find The Area Of A Rectangle With Variables

Many students face difficulty when it comes to finding the area of a rectangle in a coordinate plane. You can follow these steps to know how to find the area of a rectangle with variables.

1. First, determine the coordinates of a rectangle A(X1, Y1), B(X2, Y2), C(X3, Y3), and D(X4, Y4).
2. In the coordinate plane, the side AB and CD will represent the length of the rectangle.
3. While the side AD and BC will represent the width of the rectangle.
4. Using the distance formula: distance =√(x2−x1)2+(y2−y1)2, find the values of AB, CD, AD, and BC.
5. Once you find the values of the length and width, substitute them in the area of the rectangle formula.
6. Here, multiple the length and width of the rectangle to get its area.

In a rectangle, side AB = CD (width) and the side AD = BC (length). While using the distance formula, make sure you do not neglect the positive and negative coordinate planes.

## Find The Area Of A Rectangle With The Perimeter

Sometimes, only one side of a rectangle and its perimeter are given. You can follow these steps to know how to find the area of a rectangle with the perimeter.

1. First, recall the formula of the area of a rectangle with a perimeter which is:

A = P(l/2) –l2

1. Here, l is the length and P is the perimeter of the rectangle.
2. Now, substitute the values of the length and the perimeter of the rectangle into this formula.
3. The final value obtained will be the area of the rectangle.

In some cases, the value of the width of a rectangle is given. Simply use the A = P(w/2) – w2 formula to find the area of the rectangle surface.

However, you can even use the perimeter of a rectangle formula : P = 2l + 2w. This will help you to determine the value of the missing side of the rectangle. Once you find the values of both sides, you can easily find out the rectangle’s area.

After understanding how to find the area of a rectangle, let’s learn to find the values of length and breadth.

## Find The Length And Breadth Of A Rectangle

Students get confused when the length and breadth of the rectangle are missing but its area and perimeter are given. Here, I’ll teach you how to find the length and width of a rectangle when given the perimeter and area.

• ### Area And Perimeter

When the area and perimeter of a rectangle are known, you can use this formula: l = P/4 ± ¼ √P2 – 16A. Substitute the values of A and P to obtain the value of l.  You’ll find the value of width by using this formula w = P/2 – l. Substitute the value of P and l to get the value of w.

However, you can check this video to know how to find the length and breadth of a rectangle when given the area. You can even use the area of a rectangle calculator to find the values of length and breadth.

## Find The Perimeter Of A Rectangle

By far, I hope you’ve understood how to find the area of a rectangle in detail. Let us now find out the perimeter of a rectangle. A perimeter is defined as the length of the boundary of a figure or area.

Follow these steps to know how to find the perimeter of a rectangle.

1. Before we start, recall the perimeter of the rectangle formula which is: P = 2 x (l + w).
2. Here, P refers to the perimeter, l is the length, and w is the width of the rectangle.
3. Next, determine the values of l and w  using a ruler.
4. Substitute all the values in the formula.
5. The final value obtained will be the perimeter of the rectangle.

Instead of multiplying l and b with 2, you can even add (l + l + w + w) to get the perimeter of the rectangle.

## Find The Area Of A Square And Triangle

In this section, I’ll teach you how to find the area of a triangle and a square. Let us first check out how to find the area of a square.

• ### Square

In a square, all four sides are equal to each other. You can easily find the area of a square by using this formula: A = a2. Simply substitute the value of a (side) to obtain the area of a square.

• ### Triangle

The area of a triangle can be defined as the total region enclosed by the three sides of a triangular surface. Using this formula: Area = ½ x base x perpendicular height, you can find the area of an equilateral triangle.

## FAQ

### What Is The Formula Of Finding The Area Of A Rectangle?

The area of a rectangle is length ✕ width. So, width = area/length, i.e., 24 square units/4 units or 6 units.

### What Are Two Ways To Find The Area Of A Rectangle?

Area is measured in square units such as square inches, square feet or square meters. To find the area of a rectangle, multiply the length by the width. The formula is: A = L * W where A is the area, L is the length, W is the width, and * means multiply.

### What Is The Easiest Way To Find Area?

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.

### Is Rectangle A Square?

A rectangle is a quadrilateral, all of whose angles are equal i.e. right angles. Square, apart from all equal angles, also has all sides equal. Hence, square is a special case of rectangle. In other words rectangle is sometimes a square (when all sides too are equal).

### What Is A Rectangle Called In Math?

What Else Can We Call a Rectangle? Since, all the angles of a rectangle are equal, we also call it an equiangular quadrilateral. A quadrilateral is a 4-sided closed shape. Since, a rectangle has parallel sides, we can also call it a right-angled parallelogram.

## Conclusion

In the above post, I’ve explained how to find the area of a rectangle in square inches. The area of a rectangle is the product of the sides of a rectangle. It can be easily calculated by using this formula: Area = Length x width (breadth). You can also use the Pythagoras theorem to calculate the missing sides of the rectangle and then its area. The process of finding the area of a rectangle with variables and perimeter is a bit different. Thus, you can now easily calculate the areas of any rectangular surface by understanding how to find the area of a rectangle.

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