Surface Area Of A Rectangular Prism Formula

Surface Area Of A Rectangular Prism Formula

The total area or region that is covered by a rectangular prism’s six sides is known as its surface area. Solids called prisms have identical polygon bases and flat parallelogram sides. Prisms come in a variety of shapes, including triangles, squares, rectangles, pentagons, hexagons, and more. Students will discover more about the Surface Area of Rectangular Prism Formula in the article posted on the Extramarks website and mobile application.

Students just need to add the surface areas of the prism’s faces to determine the Surface Area of Rectangular Prism Formula. An area in a rectangular prism can be one of two types: 

• Surface Area Overall 
• Area of Lateral Surface

The notes and solutions for the Surface Area of Rectangular Prism Formula are also made available in Hindi for students of various other boards. Comprehension of the Surface Area of Rectangular Prism Formula is made easier with the help of these notes, thanks to Extramarks experts. The notes and solutions based on the Surface Area of Rectangular Prism Formula have been prepared in accordance with the NCERT Syllabus, emulating the structure of the NCERT books.

Surface Area of a Rectangular Prism

The Surface Area of Rectangular Prism Formula is the overall region or area that is covered by all of its faces. A three-dimensional form is a rectangular prism. It has six faces, each of which is rectangular in shape. Consequently, a rectangular prism’s two bases must likewise be rectangles. For instance, we may compare the Surface Area of Rectangular Prism Formula to the surfaces of the items listed on the Extramarks website and mobile application, such as a book, an aquarium with a cuboid shape, a box, etc.

The notes and solutions based on the Surface Area of Rectangular Prism Formula have been curated by Extramarks experts after great consideration and research on the previous years question papers. The framework of the notes designed by Extramarks experts is very easy to understand and comprehend. The notes are extremely internet-compatible and students can also download them for offline study and reference.

Let’s assume, for illustration, that a box has to be wrapped as a present. Calculate how much wrapping paper will be required to completely cover it, according to the students. They must first be aware of the total area of the box’s six surfaces (four lateral side surfaces, top surface, and bottom surface). The surface area of a rectangular prism is the sum of the six surfaces. 

Right rectangular prisms and oblique rectangular prisms are two different types of rectangular prisms. While the bases of an oblique rectangular prism are not arranged one atop the other, the bases of a right rectangular prism are perpendicular to one another.

The notes and solutions based on the Surface Area of Rectangular Prism Formula will thereby help students better comprehend situations like the one mentioned above.

Surface Area of Rectangular Prism Formula

Finding the total of the areas of the prism’s faces is all that is necessary to get the Surface Area of Rectangular Prism Formula. Two different regions are possible in a rectangular prism: 

• Total Area of Surface 
• Lateral Surface Area

Rectangular prism’s total surface area 

Finding the sum of the areas of all six sides of a rectangular prism will yield its entire surface area. The following is the formula for calculating a rectangular prism’s surface area: 

A rectangular prism’s total surface area is equal to 2 (lb + bh + lh) square units,

• l = Length of the rectangular prism
• b = Breadth of the rectangular prism
• h = Height of the rectangular prism

Note: Square units are used to measure the rectangular prism’s area.

The notes and solutions based on the Surface Area of Rectangular Prism Formula have been compiled by some of the top subject-matter experts working in collaboration with Extramarks to make learning easier and fun for students.

The Surface Area of Rectangular Prism Formula notes and solutions are extremely student-friendly, dynamic, diverse and varied in nature. Experts make sure that the notes are updated according to the CBSE NCERT syllabus and pertain to the framework of the NCERT books. 

The Hindi version of the Surface Area of Rectangular Prism Formula notes and solutions has been compiled by some of the most skilled translators at Extramarks. The Surface Area of Rectangular Prism Formula solutions can be used by students to take personal notes.

Below is an overview of the kind of examples that have been presented with reference to the Surface Area of Rectangular Prism Formula provided by Extramarks.

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.

Total Surface Area of Rectangular Prism

The Surface Area of Rectangular Prism Formula is given by:

SA = 2 (lh +wh + lw) Square units.

The size of a rectangular prism’s surface determines how much of its interior is revealed. Square units are used to express surface area. The lateral surface area (LSA) and twice the base area of a rectangular prism add up to the total surface area of the prism. 

The Surface Area of Rectangular Prism Formula is LSA + 2 (base area) [Square units]. 

The total surface area of all the rectangular prism’s sides, except the base, makes up the lateral surface area. Any right rectangular prism’s lateral surface area is equal to the base’s perimeter multiplied by the prism’s height. 

The lateral surface area is therefore equal to P x h [Square units].

Where 

P is the base’s perimeter. 

h be the prism’s height 

The rectangular prism’s outside edge is, 

P = 2 (l + w) 

Therefore, a rectangular prism’s lateral surface area (LSA) is equal to 2 (l + w) h square units. 

Hence, 

TSA is calculated as follows: TSA = LSA + 2 (Base Area) = 2 (l + w) h + 2 (l x w) = 2 lh + 2 wh + 2 lw [Square units] 

Consequently, the Surface Area of Rectangular Prism Formula is as follows: 

A Surface Area of Rectangular Prism Formula is equal to 2 (lh + wh + lw) square units.

The Surface Area of Rectangular Prism Formula has been mentioned and highlighted in the notes and solutions for Surface Area of Rectangular Prism Formula provided by Extramarks experts. These notes and solutions based on the Surface Area of Rectangular Prism Formula can be used by students for self-study purposes. The notes and solutions based on the Surface Area of Rectangular Prism Formula also contain high-quality illustrations and diagrams to help students better understand the concepts clearly. Examples have been provided wherever needed throughout the solutions for the Surface Area of Rectangular Prism Formula provided by Extramarks.

Lateral Surface Area of a Rectangular Prism

A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. It also goes by the name cuboid. Six faces, each with a rectangle form and twelve edges, make up a rectangular prism. It is referred to as a prism because of the length of its cross-section. The study of forms and the arrangement of objects is known as Geometry. The Surface Area of Rectangular Prism Formula is similar to those of other three-dimensional forms. The prism’s net area is equal to its surface area. Students go through a rectangular prism’s definition, kinds, surface area, and volume in more detail in the article published on the Extramarks website and mobile application.

The total surface area of all the rectangular prism’s sides, except the base, makes up the lateral surface area. Any right rectangular prism’s lateral surface area is equal to the base’s perimeter multiplied by the prism’s height. 

The lateral surface area is therefore equal to P x h [Square units]. 

Where 

P is the base’s perimeter. 

h be the prism’s height 

The rectangular prism’s outside edge is, 

P = 2 (l + w) 

Therefore, a rectangular prism’s lateral surface area (LSA) is equal to 2 (l + w) h square units.

The notes and solutions for the Surface Area of Rectangular Prism Formula can be downloaded in high quality. They are also descriptive, comprehensive and detailed in nature. The notes and solutions based on the Surface Area of Rectangular Prism Formula prides curated assessments to evaluate the progress of students.

Below is an overview of the examples that have been provided for the LSA of a rectangular prism on the Extramarks website and mobile application:

Question 1: Find the volume of a rectangular prism whose length, width, and height are 8 cm, 6 cm, and 4 cm, respectively.

Solution:

Given:

Length, l = 8 cm

Width, w = 6 cm

Height, h = 4 cm

The formula to find the volume of a rectangular prism is,

V = Length x Width x Height cubic units

V = 8 x 6 x 4 cm3

V = 192 cm3

Therefore, the volume of a rectangular prism is 192 cm3.

Question 2: Find the surface area of a rectangular prism whose length, width, and height are 8 cm, 6 cm, and 4 cm, respectively.

Solution: Given:

Length, l = 8 cm

Width, w = 6 cm

Height, h = 4 cm

The formula to find the area of a rectangular prism is,

A = 2 (lh +wh + lw)

A = 2 (8×4+6×4+8×6)

A = 2(32+24+48)

A = 2(104)

A = 208 sq. cm.

Students can find more examples like the ones above by registering themselves on the Extramarks website and mobile application, thereby gaining access to a number of solved examples and practice questions to prepare better for their final examinations.

How to Calculate the Surface Area of a Rectangular Prism?

These procedures may be used to determine a Surface Area of Rectangular Prism Formula: 

Step 1: Verify whether or not the rectangular prism’s dimensions are presented in the same units. If not, change them to the same measurement system. 

Step 2: After the dimensions have been converted to the same units, realise that you must compute the lateral surface area or the total surface area in accordance with the circumstances. 

Step 3: Use the Surface Area of Rectangular Prism Formula for total surface area, or 2 (lb + bh + lh), to get the lateral surface area. 

Step 4: Convert the unit to square units and write down the values that result.

Students may comprehend how to calculate a Surface Area of Rectangular Prism Formula with the aid of an example after they are familiar with the formula and procedure for doing so.

Surface Area of Rectangular Prism Examples

Once students learn how to calculate the surface area of a rectangular prism, they can learn better with the help of an example like the one given below:

 Example: Calculate the least amount of wrapping paper needed to cover a rectangular present box with the following dimensions: 

Dimensions: L = 24 inches 

B = 15 inches for breadth. 

h = 20 inches tall 

Solution: In this instance, students must determine the box’s entire surface area. They may compute it by doing the procedures below: 

Step 1: Calculate the size of the box’s top and bottom faces. 

Since the size of the top and bottom surfaces of the box are identical, students may simply double the area of any surface. 

2lb is equal to 2 (24 15) = 2 360 = 720 inch2.

Step 2: Next, we measure the size of the box’s side faces.

2bh = 2 × (15 × 20) = 2 × 300 = 600 inch2

2lh = 2 × (24 × 20) = 2 × 480 = 960 inch2

Step 3: to get the box’s total surface area, add the areas of all six faces.

2 (lb + bh + lh) = 2lb + 2bh + 2lh = 720 + 600 + 960 = 2280 inch2.

Practice Questions on Surface Area of Rectangular Prism

1. Calculate the area of a rectangular prism whose dimensions are given for the length, width, and height. 

3, 4, and 5 cm, 8 cm, 10 cm, 2.5 cm, 6 cm 

6, 2, 4, and 9 centimetres. Find the volume of the following-sized rectangular prism. 

Size: 3 x 4 x 5 cm 

2.5 cm, 6 cm, and 9 cm 

5 x 8 x 10 cm 

6.2 x 4.4 x 9 centimetres 

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