# Finding the Surface Area of a Pyramid

Surface Area of a Pyramid Calculator: Are you looking for the process on how to find the surface area of a pyramid? Then, you are on the right page. Here, we have compiled a stepwise procedure to calculate the total surface area of a right rectangular pyramid along with direct formula and derivation.

If you want to do your lengthy calculations in a quick way then go with our fee online handy surface area of a pyramid calculator and make your calculations at a faster pace. Furthermore, we have given complete details about the pyramid surface area like definition, how to find easily, and steps to use our little handy pyramid surface area calculator tool along with solved examples.

## What is the Surface Area of a Pyramid?

The surface area of a pyramid is equal to the sum of the areas of each side of the pyramid. The base of the pyramid has the area ‘l x w’, and the slant height on the length and slant height on the width is represented as ‘sl’ and ‘sw’. Hence, the formula to calculate the surface area of a pyramid is given below:

 Surface Area of  Pyramid (A) = lw + l (√(w/2)²+(h)²) + w (√(l/2)²+(h)²)

Now, you know the formula to find out the total surface area of a pyramid. Just follow the below simple steps to calculate the pyramid surface area and make your calculations easier and faster.

### How to Find the Surface Area of a Pyramid?

In order to calculate the total surface area of a pyramid, first, you need to take the given inputs for base length, base width, and height. Thereafter, consider the surface area of the pyramid formula which is given under,

A = l * w + l (√((w/2)²+(h)²)) + w (√((l/2)²+(h)²))

where A = total surface area of a pyramid

l = base length

w = base width

h = height

Now, applying all these input values in the surface area of a pyramid formula, you will get the output that you are required in the same unit metric.

Note: If you take all three input unit metric the same, then you will get the same unit metric as an output. Else, you need to perform unit conversions and make all three in one required unit metric and then get the output in the respective unit measurements.

For a better way of understanding, check out the below given worked example to find the surface area of a pyramid for given inputs. have a glance at it and enhance your concept knowledge in a better way and do calculations much faster.

Example:

Calculate the surface area of a pyramid whose length, width, and height is 5 cm, 6 cm, 7 cm respectively?

Solution:

Given,

Base Length of a Pyramid = 5 Cm

Base Width of a Pyramid = 6 Cm

Height of a Pyramid = 7 Cm

Formula to find the Surface Area of a Pyramid is given by

A = l * w + l (√((w/2)²+(h)²)) + w (√((l/2)²+(h)²))

Substitute the given base length and width, height values in the formula and perform the math calculations:

A = 5 x 6 + 5 (√((6/2)²+(7)²)) + 6 (√((5/2)²+(7)²))

Now, split into three parts and calculate each one

Multiply 5 cm and 6cm at first

A = 30 cm² + 5 (√((6/2)²+(7)²)) + 6 (√((5/2)²+(7)²))

The square root of (√((6/2)²+(7)²)) is 7.6157731

Now, put the value in the respective place and calculate the other square root also,

A = 30 cm² + 5 x 7.6157731 + 6 x ((√((5/2)²+(7)²))

The square root of (√((5/2)²+(7)²)) is 7.4330344

Put The values in Area Formula:

A= 30.0 + 5 x 7.6157731 + 6 x 7.4330344

Multiply 5 and 7.6157731

A= 30.0 + 38.0788655 + 6 x 7.4330344

Multiply 6 and 7.4330344

A= 30.0 + 38.0788655 + 44.5982062

A=68.0788655 + 44.5982062

A= 112.6770718 cm²

Therefore, The surface area of a Pyramid for length 5cm, width 6cm, and height 7cm is 112.6770718 cm².

### Steps to Use Surface Area of a Pyramid Calculator

The instructions that you need to follow to use our online handy Surface area of a pyramid calculator are mentioned over here:

• First, give your respective input values in the fields of ‘Enter the base length, enter the base width, and enter the height’.
• Choose the required unit metrics for length, width, and height.
• Now, Click on the Area Button and make the calculations done internally to display the output.
• Later, the surface area of a pyramid output will be displayed on the page within less time.

### FAQs on Finding Surface Area of a Pyramid

1. How do you find the total surface area of a pyramid?

To determine the surface area of a pyramid, begin with multiplying the perimeter of the pyramid by its slant height. Next, divide that number by 2. Lastly, add the number you get to the area of the pyramid’s base to find the surface area of a pyramid.

2. What is the formula for finding the surface area of a triangular pyramid?

In order to find the surface area of a regular triangular pyramid, we use the formula SA = A + (3/2)b * h, where A is the area of the pyramid’s base, b = the base of one of the faces, and h = height of one of the faces.

3. What is the Surface Area of a Pyramid Calculator?

Pyramid Surface Area Calculator is a free online tool that helps you to find out the total surface area of a regular or irregular pyramid by just giving the inputs and its unit metric. At last, press the Area button to display the output of a surface area of the pyramid.

4. What is the formula for a surface area of a right rectangular pyramid?

The formula for the surface area of a pyramid is A = l * w + l (√((w/2)²+(h)²)) + w (√((l/2)²+(h)²)).