# Surface Area Of A Pyramid Formula

## Surface Area Of A Pyramid Formula

A Surface Area of a Pyramid Formula is calculated by summing the areas of all of its faces. A pyramid is a three-dimensional form with a polygonal base and triangle-shaped side faces that meet at a location known as the apex or vertex. The altitude or height of the pyramid is the perpendicular distance from the peak to the centre of the base. The “slant height” is the length of the perpendicular path traced from a triangle’s apex to its base (side face). The surface area of a pyramid, the Surface Area of a Pyramid Formula, a few examples with solutions, and practice problems are all available to students.

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

What is the Surface Area of Pyramid?

A Surface Area of a Pyramid Formula is a measurement of the entire area occupied by all of its faces. Students can check out the pyramid shown on the Extramarks website and mobile application to view all of its faces as well as its peak, altitude, slant height, and base.

• Since a Surface Area of a Pyramid Formula equals the total of its face areas, it is expressed in square units like m2, cm2, in2, ft2, etc. The Lateral Surface Area (LSA) and the Total Surface Area are the two different types of surface areas that make up a pyramid (TSA).
• The total area of a pyramid’s side faces (triangles) is the lateral surface area, or LSA.
• The LSA of the pyramid plus the Base area equals the Total Surface Area (TSA) of a pyramid.
• Without any other details, the surface area of a pyramid generally refers to the entire pyramid.

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

### Surface Area of Pyramid Formula

Finding the Surface Area of a Pyramid Formula faces and putting them together will provide the pyramid’s surface area. There is a particular Surface Area of a Pyramid Formula to determine the lateral surface area and total surface area of a regular pyramid, defined as one whose base is a regular polygon and whose height passes through the centre of the base. Consider a regular pyramid with a base area of “B,” a base perimeter of “P,” and a slant height of “l” (the height of each triangle). Then,

The pyramid’s Lateral Surface Area (LSA) equals (1/2) Pl

The TSA of a pyramid is equal to LSA plus base area, which is equal to (1/2) Pl + B.

Students must utilize the Surface Area of a Pyramid Formula for calculating the polygonal area to determine the base areas in this case. Students can understand how to arrive at the Surface Area of a Pyramid Formula for a pyramid’s surface area.

Having carefully considered and researched previous years’ question papers, Extramarks experts have crafted notes and solutions based on the Surface Area of a Pyramid Formula. Surface Area of a Pyramid Formula notes designed by Extramarks experts are easy to understand and comprehend. In addition to being extremely internet-compatible, the Surface Area of a Pyramid Formula notes can also be downloaded for offline study and reference.

### Proof of Surface Area of Pyramid Formula

The perimeter and slant height of a pyramid make up its Surface Area of a Pyramid Formula. Students can use a specific pyramid as an example to better grasp the LSA and TSA Surface Area of a Pyramid Formula for pyramids. Students think about a square pyramid with a length “a” for the base and a height “l” for the tilt.

Then,

• The base area (area of square) of the pyramid is, B = a2
• The base perimeter (perimeter of the square) of the pyramid is, P = 4a
• The area of each of the side faces (area of a triangle) = (1/2) × base × height = (1/2) × (a) × l
• Therefore, the sum of all side faces (sum of all 4 triangular faces) = 4 [(1/2) × (a) × l] = (1/2) × (4a) × l = (1/2) Pl. (Here, we replaced 4a with P which represents its perimeter.)

Hence, the Lateral Surface Area of the pyramid (LSA) = (1/2) Pl

We know that the Total Surface Area of a pyramid (TSA) is obtained by adding the base and lateral surface areas. Thus,

The total surface area of the pyramid (TSA) = LSA + base area = (1/2) Pl + B

Using these two formulas, students can derive the Surface Area of a Pyramid Formula of different types of pyramids.

### Examples on Surface Area of Pyramid

Figure 1: If a square pyramid’s base has a side length of 14 inches and a slant height of 20 inches, determine the lateral surface area of the pyramid.

Solution:

The base’s side length, a, is 14 inches.

The base’s (square) perimeter is thus given by P = 4a = 4(14) = 56 inches.

Slant height, 20-inch length

A square pyramid’s lateral surface area is given by Lateral surface area (LSA) = (1/2) Pl = (1/2) (56) 20 = 560 in2.

Consequently, the suggested pyramid has a lateral surface area of 560 in2.

Students can find more examples like the one mentioned above in the Surface Area of a Pyramid Formula on the Extramarks website and mobile application.

### Practice Questions on Surface Area of Pyramid

Q.1 The formula for a pyramid’s lateral surface area is LSA = (1/2) Pl, where “P” stands for the base’s perimeter and “l” for the slant height.

Responses

a.) True

b.) False

Q.2

If the altitude (h) and the base length (a) of a square pyramid is given, its slant height (l) can be calculated with the formula:

Responses

l2 = (a/2)2 + h2

l, 2, = (a/2), 2, + h, 2

l2 = (h/2)2 + a2

l, 2, = (h/2), 2, + a 2

Answer: l2 = a2 + h2

## 1. What is the definition of a pyramid's surface area?

A Surface Area of a Pyramid Formula is calculated as the total of all of its face areas. The total surface area (TSA), which is the sum of all the areas of the faces, and the lateral surface area (LSA), which is the sum of the areas of the side faces, are the two different types of surface areas.

## 2. What is the Pyramid's Total Surface Area?

A Surface Area of a Pyramid Formula is calculated by summing the areas of all of its faces (both the base and the side faces). The equation TSA = (1/2) Pl + B may be used to get the total surface area of a pyramid where the base perimeter is P, the base area is B, and the slant height is l.

## 3. What is the pyramid's lateral surface area?

A pyramid’s lateral surface area is equal to the sum of all of its side faces (which are triangles). The formula LSA = (1/2) Pl, where P is the base’s perimeter and l is the slant height, is used to determine a pyramid’s lateral surface area.

## 4. What is the Surface Area of a Pyramid Formula?

A pyramid has two different types of surface areas: the Surface Area of a Pyramid Formula and the lateral surface area. The following Surface Area of a Pyramid Formula is used to determine these two regions.

Surface area overall = (1/2) Pl + B

(1/2) = lateral surface area where “P” stands for the base perimeter, “B” stands for the base area, and “l” stands for the slant height.

## 5. How can students determine a Surface Area of a Pyramid Formula with Slant Height?

The slant height may be used to compute the Surface Area of a Pyramid Formula for calculating a pyramid’s surface area. The equation (1/2) Pl + B can be used to get the object’s total surface area. Think about a pyramid with a slant height of “l,” a base perimeter of “P,” and a base area of “B.” The formulae for calculating a polygon’s area may be used to determine the base area.

## 6. How can students calculate a Surface Area of a Pyramid Formula given its height (or Altitude)?

If the altitude is known, the surface area of a pyramid may be determined. Consider a pyramid with a base that is a regular polygon with side length “a,” a slant height of “l,” and an altitude of “h.” If just “a” and “h” are provided, and we still need to calculate the surface area, students must first determine the slant height. They can use the subsequent stages to comprehend this.

Step 1: Apply the Pythagoras theorem to find “l,” which is l2 = (a/2)2 + h2.

Step 2. Determine the base perimeter, or “P.”

Step 3. Locate the base area “B.”