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Area of a Rectangle Overview
Calculating surface area is a skill that can be applied in many real-world situations. Area calculations are made for scenarios such as determining the number of tiles needed to cover the bottom of a swimming pool, the amount of wrapping paper needed to wrap a gift, or the amount of square footage you have in your backyard. Situations such as these will require the use of surface area calculations.
Area of Rectangle Sample Questions
When determining the area of a rectangle, the formula A=l×w
can be applied. A represents area, l represents length, and w represents width. For example, the rectangle below has a length of 32 meters and a width of 20 meters. The area of the rectangle can be calculated by multiplying l×w, or 32×20, which is 6,400. The units associated with surface area will always be units squared. Area is the result of multiplying two dimensions, length and width, which can be represented as a power of 2. In this case, our answer would be 640 m2.
Consider the following:
You want to plant grass in your new backyard, and you currently have 645 square feet of sod available. You want to determine if this is enough grass to cover the entire yard, so you need to compare the area of the sod to the area of your yard. Your yard has a length of 25 feet and a width of 30 feet. Do you have enough sod to cover the entire yard?
This is a scenario where the area formula of a rectangle can be applied. The length of the yard is 30 feet, and the width is 20 feet. The formula states that A=l×w
, so the area of the yard is 30 ft×25 ft
which is 750 square feet. In this case, 645 square feet of sod is not enough to cover the entire yard. 105 more square feet of sod will be required.
Many area problems will be presented in the format of A=l×w
, where both length and width are provided and the area is being solved for. However, it is also common in area problems to provide the area, but have missing dimensions. For example, the area of the following rectangle is 12 cm2 and its length is 6 cm. What is the width of the rectangle?
The area formula can be applied in situations like this, but the formula will need to be manipulated in order to solve for w instead of A. The formula A=l×w becomes 12 cm2=6 cm×w, and in order to solve for w, we need to divide both sides of the equation by 6. w=2 cm
, so the width of the rectangle is 2 cm.
Consider the following:
You want to install a wire fence that surrounds your garden in order to keep deer and rabbits out. You know that the area of your garden is 210 square feet and the width is 14 feet. What is the length of the garden, and how many feet of fencing will need to be installed?
The missing length can be determined using the area formula A=l×w. The formula becomes 210 ft2=l14 ft, and when both sides of the equation are divided by 14, the length is revealed as 15 feet. From here, we can simply add the two lengths and the two widths in order to find the total amount of fencing that is required: 14+14+15+15=58 feet of fencing
.It is important to note that the formula A=l×w
only applies to the surface area of rectangles and squares. Other two-dimensional shapes will have their own unique formulas. For example, the area of a triangle is A=1/2bh, and the area of a circle is A=πr2.
How to find the surface area of a rectangle?
You can use the following formula to find the area of a rectangle.
Step 1: Multiply the length by the width.
Step 2: L X W , where L is the length and W is the width.
A square which is also a type of rectangle with all equal sides.
How to find the area of a Square?
Step 1: Multiply the length by the length itself.
Step 2: L X L = L2, where L is the length of each side.
Examples of Surface area of a Rectangle
Question 1: Find the area of the rectangle if the length is 7 cm and the width is 5 cm.
Answer: The area of the rectangle is W X L
= 7 x 5 cm2
= 35 cm2
Question 2: Find the area of the square if each side of the square is 6 cm.
Answer: The area of the square is L X L
= 6 x 6 cm2
= 36 cm2
Surface area of a rectangle equation
A rectangle is a closed figure with four sides, whose opposite sides are equal. Hence, two sides or dimensions are sufficient to describe a rectangle — its length (sometimes called height) and its width (sometimes called breadth).
The equation for the surface area of a rectangle is given by:
where:
- is the surface area of the rectangle;
- is the length of the rectangle. Usually, it refers to the longest side of the rectangle.
- is the width of the rectangle. Usually, it refers to the shortest side of the rectangle.
The SI units for area are m2 or sq m (square meters), and its imperial units are ft2 or sq ft (square feet). Always ensure that the length and width are expressed in the same units before using the surface area formula of a rectangle.
For example, a rectangle with 5 m length and 2 m breadth (or width) would have a surface area of 5×2=10 m2.
🔎 Since a rectangle is a 2D geometry, it is sufficient to refer to its surface area as area.
How to find the surface area of a rectangle?
To find the surface area of a rectangle, you require its length and width:
- Convert the length and width into the same unit. We must measure them both in the same unit. For example, if the length is
5 m, and width is2 ft, convert both to eithermorft. - Multiply this length and width to obtain the area in corresponding units.
- Double-check your answer using the surface area of a rectangle calculator.
How do I use this surface area of a rectangle calculator?
This surface area of a rectangle calculator is simple to use:
- Enter the length of the rectangle in its appropriate field. Ensure you’ve picked the suitable units.
- Enter the width (or breadth) of the rectangle in its appropriate field. Again, ensure that you’ve picked the correct units.
- This surface area of a rectangle will automatically find the surface area of the rectangle and display the result in the appropriate field.
So now you know how to find the area of a rectangle!
FAQ
How do I calculate the area of my monitor screen?
Most monitor screens are rectangular in shape. To calculate the area of your monitor screen, follow these simple steps:
- Measure the length and width of your monitor with a monitor or measuring scale. Alternatively, you can get these dimensions from the product description.
- Multiply the length and width together to obtain the surface area of your monitor screen.
- Rejoice in your newfound knowledge of your screen’s area.
How many acres to one hectare?
There are 2.471 acres to one hectare. An acre is a unit of land and is roughly equal to 4047 sq m. A hectare is a unit of land equal to 10,000 sq m.
Surface Area of Rectangular Prism
The surface area of a rectangular prism is the total area or region covered by its six faces. Prisms are solids with flat parallelogram sides and identical polygon bases. There are different types of prisms, namely – triangular prisms, square prisms, rectangular prisms, pentagonal prisms, hexagonal prisms, etc. In this article, you will learn more about the surface area of rectangular prisms.
Surface Area of a Rectangular Prism
The total region or area covered by all the faces of a rectangular prism is defined as the surface area of a rectangular prism. A rectangular prism is a three-dimensional shape. It has six faces, and all the faces are rectangular-shaped. Therefore, both the bases of a rectangular prism must also be rectangles. For example, we can relate the surface area of a rectangular prism with the surfaces of the objects given below: a book, cuboid-shaped aquarium, box, etc.
For example, let’s say there is a box that needs to be gift-wrapped. You need to calculate the amount of wrapping paper that will be needed to cover it. First, you will need to know the sum of the areas of the six surfaces of the box (four lateral side surfaces, top surface, and bottom surface). This total area of the six surfaces is called the surface area of a rectangular prism.
A rectangular prism can be classified as a right rectangular prism or an oblique rectangular prism. In the right rectangular prism, bases are perpendicular to each other whereas, in an oblique rectangular prism, the bases are not aligned one above the other. Let us see the basic formulas to calculate the total surface area and lateral surface area of a rectangular prism in the next section.
Surface Area of Rectangular Prism Formula
To calculate the surface area of a rectangular prism, we need to simply find the sum of the areas of the faces of the prism. A rectangular prism can have two types of areas:
- Total Surface Area
- Lateral Surface Area
Total Surface Area of Rectangular Prism
The total surface area of a rectangular prism can be calculated by finding the total area of all six faces. The formula to find the surface area of a rectangular prism is given as,
Total surface area of a rectangular prism = 2(lb + bh + lh) square units
where,
- l = Length of the rectangular prism
- b = Breadth of the rectangular prism
- h = Height of the rectangular prism
Note: The unit of measurement of the area of the rectangular prism is square units.
Lateral Surface Area of a Rectangular Prism
The lateral surface area of a rectangular prism can be calculated by finding the sum of all the lateral faces of the prism, i.e. the total area excluding the area of the bases. The formula to find the surface area of a rectangular prism is given as,
Lateral surface area of a rectangular prism = 2(l + b) h square units
where,
- l = Length
- b = Breadth
- h = Height of the rectangular prism
Example: Determine the total surface area of a rectangular prism with the following dimensions:
- Length (l) = 8 inches
- Breadth (b) = 5 inches
- Height (h) = 7 inches
Solution: The total surface area of the rectangular prism is given by: 2(lb + bh + lh) = 2(8 × 5 + 5 × 7 + 8 × 7) = 2(40 + 35 + 56) = 2 × 131 = 262 inch2.
How to Calculate the Surface Area of a Rectangular Prism?
The surface area of a rectangular prism can be calculated using the following steps:
- Step 1: Check if the given dimensions of the rectangular prism are in the same units or not. If not, convert them into the same units.
- Step 2: Once the dimensions are in the same units, understand the need to calculate the lateral surface area or the total surface area according to the given situation.
- Step 3: Implement the formula for lateral surface area 2h(l + b), or total surface area, 2 (lb + bh + lh).
- Step 4: Write the unit as square units along with the values thus obtained.
Now that we know the formula and method to calculate the surface area of a rectangular prism, let us now understand how to calculate it with the help of an example.
Example: Determine the minimum area of the wrapping paper required to wrap a rectangular gift box with dimensions as given below:
- Length, l = 24 inches
- Breadth, b = 15 inches
- Height, h = 20 inches
Solution: In this case, we have to find the total surface area of the box. It can be calculated by following the steps given below:
Step 1: Determine the area of the top and bottom faces of the box.
The area of the bottom and the top surfaces are equal, therefore we can simply twice the area of the top or bottom of the box.
2lb = 2 × (24 × 15) = 2 × 360 = 720 inch2
Step 2: Next, we determine the area of the side faces of the box.
2bh = 2 × (15 × 20) = 2 × 300 = 600 inch2
2lh = 2 × (24 × 20) = 2 × 480 = 960 inch2
Step 3: Add the areas of all six faces to determine the total surface area of the box.
2(lb + bh + lh) = 2lb + 2bh + 2lh = 720 + 600 + 960 = 2280 inch2.
Challenging Question:
Two boxes each of dimensions (4 inches × 5 inches × 6 inches) are joined together face to face to make a rectangular prism box. Determine the surface area of the newly formed box.
Tips and Tricks:
- A rectangular prism with all sides equal is called a cube.
- A rectangular prism in which the faces are not perpendicular to each other is called an oblique rectangular prism.
- If all the edges of a rectangular prism are equal, then the surface area of the prism will be equal to 6 times the area of each face.
- If all the edges of a rectangular prism are equal to ‘l’, then the volume of the prism is ‘l3‘.
Surface Area of Rectangular Prism Examples
Example 1: Emily needs to buy some cardboard to build a box without a lid 7 feet long, 5 feet wide, and 9 feet high. How much cardboard should she buy?
Solution:
The dimensions of the box are as follows:
- Length, l = 7 feet
- Breadth, b = 5 feet
- Height, h = 9 feet
To find the area of cardboard required, we need to find the total area of the open box. The area of an open box (a box without a lid), can be determined by calculating the total area of 5 surfaces:
- Base area: lb
- Area of 4 lateral faces or lateral surface area: 2(l + b)h = 2lh + 2bh
⇒ Total surface area of the rectangular prism (open box) = lb + 2lh + 2bh
= 7 × 5 + 2 × 7 × 9 + 2 × 5 × 9
= 35 + 126 + 90
= 251 inch2
Answer: Emily should buy 251 inch2 of cardboard.
Example 2: The total surface area of a rectangular prism is 76 ft2 with a base area of 10 ft2 and the perimeter of the base being 14 ft. Using the surface area of a prism formula, determine its height.
Solution:
Let l, b, h be the length, breadth, and height of the rectangular prism respectively.
Base area, lb = 10 ft2
Base perimeter, 2(l + b) = 14 ft
Surface area = 76 ft2
Using the surface area of a rectangular prism formula,
Total surface area = 2(lb + bh + lh) = 76 ft2
or, 2lb + 2(l+b)h = 76 ft2
Substituting values, we get,
2 × 10 + 14 × h = 76
20 + 14 × h = 76
14 × h = 56
h = 56/14 = 4 ft
Answer: Height of the prism is 4 ft.
FAQs on Surface Area of Rectangular Prism
What is the Surface Area of a Rectangular Prism?
The surface area of a rectangular prism is defined as the area of all the rectangular faces of the prism. It can be of two types: total surface area and lateral surface area. The total surface area of a rectangular prism refers to the area of all six faces, while the lateral surface area covers the area of only the lateral faces and thus doesn’t include the base areas.
How do you find the Surface Area of a Rectangular Prism?
The surface area of a rectangular prism can be calculated by adding the area of the rectangular faces of the prism. The following steps depict how to find the area,
- Step 1: Note down the dimensions of the rectangular prism and check that they are in the same units.
- Step 2: Apply the formula to calculate the total surface area or the lateral surface area, according to the situation given in the problem.
TSA of rectangular prism = 2(lb + bh + lh)
LSA of rectangular prism = 2(l + b)h - Step 3: Represent the obtained answer in square units.
What is the Formula for Calculating the Surface Area of a Rectangular Prism?
The formula to calculate the total surface area of a rectangular prism is given as, TSA of rectangular prism = 2(lb + bh + lh), where, l is length, b is breadth and h is the height of the prism. Also, the lateral surface area of a rectangular prism can be calculated using the formula, LSA of rectangular prism = 2(l + b)h square units.
How to Find the Dimensions of a Rectangular Prism With the Surface Area?
We can calculate the missing dimension of a rectangular prism using area by substituting the given values into the formula of the surface area of a rectangular prism, and further solving to obtain the result. The formulas to calculate the surface area of the rectangular prism are given as,
Total surface area = 2(lb + bh + lh) square units
Lateral surface area = 2(l + b)h square units
where,
- l = Length
- b = Breadth
- h = Height
What Happens to the Surface Area of Rectangular Prism When Each of the Dimensions is Doubled?
The surface area of a rectangular prism quadruples when each of the dimensions is doubled. Hence, we obtain surface area 4 times the original one in this case.
What Unit is Used for Surface Area of Rectangular Prism?
The unit of measurement for the surface area of a rectangular prism is square units or (unit)2. The SI unit is m2, where the other units can be in2, ft2, cm2, etc.
The workers at a candy factory have been tasked with finding out how much material is required to cover the factory’s famous candy bar. The candy bar measures 5 inches long, 2 inches wide, and 1 inch in height. What size wrapper will be required to cover the candy bar?
In this concept, you will learn how to calculate the surface area of a rectangular prism.
Finding the Surface Area of a Rectangular Prism
Area is the space that is contained in a two-dimensional figure. Surface area is the area of all the sides and faces of a three-dimensional figure. Imagine wrapping a solid figure in wrapping paper, like a present. The amount of wrapping paper needed to cover the figure represents its surface area.
To find the surface area, you calculate the area of each face or side and then add these areas together.
One way to do this is to use a net, since a net is a picture of an unfolded solid, representing each of its faces and/or sides. Do this by finding the area of each face or side of the net, and then adding all of the areas together.
You can use this process with prisms of all different kinds. Let’s look at a net for a rectangular prism.
Again, the surface area of this prism is 158 square inches. This formula just saves a little time by allowing you to calculate the area of pairs of faces at a time.
Examples
Example 1
Earlier, you were given a problem about the candy factory workers, who need to figure out how much wrapper is needed to cover their famous candy bar.
First, plug the dimensions of the candy bar into the formula for surface area of a rectangular prism and multiply the values within the brackets:
The answer is the candy bar will require 34 square inches to completely cover the candy bar.
Example 2
What is the surface area of the figure below?
All of the faces of this prism are rectangles, so you can use the formula for finding the surface area of a rectangular prism as follows.
First, plug the values given above into the surface area formula and multiply the values together within each of the parentheses:
Then, add the values together for the final answer. Remember to include the unit of measurement:
The answer is the rectangular prism has a surface area of 938 square centimeters.
Example 3
Find the surface area of a rectangular prism with a length of 8 in, width of 4 inches, height of 6 inches.
First, plug the values given above into the surface area formula and multiply the values together within each of the parentheses:
Then, add the values together for the final answer. Remember to include the unit of measurement:
The answer is the surface area for this rectangular prism is 208 square inches.
Example 4
Find the surface area of a rectangular prism with a length of 5 ft, width of 4 ft, height of 2 ft
First, plug the values given above into the surface area formula and multiply the values together within each of the parentheses:
The answer is the surface area for this rectangular prism is 76 square inches.
Review
Use the formula for surface area to find the surface area of each rectangular prism.
- A rectangular prism with a length of 10 in, width of 8 in and height of 5 inches.
- A rectangular prism with a length of 8 in, width of 8 in and height of 7 inches.
- A rectangular prism with a length of 12 m, width of 4 m and height of 6 meters.
- A rectangular prism with a length of 10 in, a width of 6 in and a height of 7 inches.
- A rectangular prism with a length of 12 m, a width of 8 m and a height of 5 meters.
- A rectangular prism with a length of 9 ft, a width of 7 feet and a height of 6 feet.
- A rectangular prism with a length of 10 m, a width of 8 m and a height of 2 m.
- A rectangular prism with a length of 6 ft, a width of 5 feet and a height of 3 feet.
- A rectangular prism with a length of 3 feet, a width of 6 feet and a height of 2 feet.
- A rectangular prism with a length of 4 feet, a width of 4 feet and a height of 4 feet.
- A rectangular prism with a length of 12 feet, a width of 9 feet and a height of 7 feet.
- A rectangular prism with a length of 14 feet, a width of 11 feet and a height of 10 feet.
- A rectangular prism with a length of 18 feet, a width of 16 feet and a height of 12 feet.
- A rectangular prism with a length of 22 meters, a width of 18 meters and a height of 10 meters.
- A rectangular prism with a length of 21 meters, a width of 18 meters and a height of 17 meters.
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