Â  Â  Â  Â
Â  Â  Â  Â  Â  Â

# Math Examples of Pyramids

• ## Calculate the lateral surface area of a triangular pyramid where base measure of pyramid is 11 inch and the slant height of pyramid is 13 inch?

The formula for finding the lateral surface area of a pyramid is given by:
Lateral surface area of pyramid = ½ * p * h;
Where, ‘p’ is the perimeter and ‘h’ is the slant height of pyramid.
Given, length = 11 inch;
Slant height = 13 inch;
LSA =?
First we find the perimeter of a pyramid:
Perimeter of a triangular pyramid is a + b + c;
Perimeter = 11 + 11 + 11;
Perimeter = 33 inch;
On putting these values in the formula we get:
LSA = ½ * p * h;
LSA = ½ * 33 * 13;
LSA = ½ * 429;
LSA = 214.5 inch2;
So LSA of triangular pyramid is 214.5 inch2.

## Calculate the lateral surface area of a triangular pyramid where base measure of pyramid is 17 inch and the slant height of a pyramid is 16 inch?

The formula for finding the lateral surface area of a pyramid is given by:
Lateral surface area of pyramid = ½ * p * h;
Where, ‘p’ is the perimeter and ‘h’ is the slant height of a pyramid.
Given, length = 17 inch;
Slant height = 16 inch;
LSA = ?
First we find the perimeter of pyramid:
Perimeter of a triangular pyramid is a + b + c;
Perimeter = 17 + 17 + 17;
Perimeter = 51 inch;
On putting these values in the formula we get:
LSA = ½ * p * h;
LSA = ½ * 51 * 16;
LSA = ½ * 816;
LSA = 408 inch2;
So LSA of a triangular pyramid is 408 inch2.

## Calculate the slant height of pyramid where one side length of pyramid is 22 inch and lateral surface area of a triangular pyramid is 130 inch2

The formula for finding the lateral surface area of a pyramid is given by:
Lateral surface area = ½ * p * h;
Given, length = 22 inch;
LSA = 130 inch2;
Slant height =?
First we find the perimeter of a pyramid:
Perimeter of a triangular pyramid is a + b + c;
Perimeter = 22 + 22 + 22;
Perimeter = 66 inch;
On putting these values in the formula we get:
LSA = ½ * p * h;
130 = ½ * 66 * h;
130 = 33 * h;
H = 130 / 66;
H = 1.96 inch;
So height of pyramid is 1.96 inch.

## Calculate the lateral surface area of triangular pyramid where base measure of a pyramid is 15.9 inch and the slant height of pyramid is 14.5 inch?

The formula for finding the lateral surface area of a pyramid is given by:
Lateral surface area of pyramid = ½ * p * h;
Where, ‘p’ is the perimeter and ‘h’ is the slant height of a pyramid.
Given, length = 15.9 inch;
Slant height = 14.5 inch;
LSA =?
First we find the perimeter of a pyramid:
Perimeter of a triangular pyramid is a + b + c;
Perimeter = 15.9 + 15.9 + 15.9;
Perimeter = 47.7 inch;
On putting these values in the formula we get:
LSA = ½ * p * h;
LSA = ½ * 47.7 * 14.5;
LSA = ½ * 691.65;
LSA = 345.82 inch2;
So the LSA of a triangular pyramid is 345.82 inch2.

## Calculate the slant height of pyramid where one side length of pyramid is 25 inch and lateral surface area of a triangular pyramid is 90 inch2?

The formula for finding the lateral surface area of a pyramid is given by:
Lateral surface area = ½ * p * h;
Given, length = 25 inch;
LSA = 90 inch2;
Slant height =?
First we find the perimeter of pyramid:
Perimeter of a triangular pyramid is a + b + c;
Perimeter = 25 + 25 + 25;
Perimeter = 75 inch;
On putting these values in the formula we get:
LSA = ½ * p * h;
90 = ½ * 75 * h;
90 = 37.5 * h;
H = 90 / 37.5;
H = 2.4 inch;
So the height of a pyramid is 2.4 inch.

## Find the total surface area of a pyramid which has perpendicular height of 6.2 inch and base edge of 20 inch?

The formula for finding the total surface area of a pyramid = area of the base + 4 * area of triangular face.

Given, Height = 6.2 inch;
Base edge = 20 inch;
TSA =?
Here we use pythagoras theorem for the Right Triangle AOM, we get:
b2 = (6.2)2 + (10)2;
b2 = 38.44 + 100;
b = √ 138.44;
b = 11.76 inch;
Area of triangle ASR = ½ * b * h;
Area of triangle ASR = ½ * 20 * 11.76;
Area = 117.66 inch2;
Now area of Square base = s2
Area = (20)2;
Area = 400 inch2;
Now put these values in the formula and we will get TSA of pyramid.
TSA = area of the base + 4 * area of triangular face;
TSA = 400 + 4 * 177.66;
TSA = 1110.64 inch2.
So TSA of pyramid is 1110.64 inch2.

## Find the total surface area of a pyramid which has perpendicular height of 15 inch and base edge of 34 inch?

The formula for finding the total surface area of a pyramid = area of the base + 4 * area of triangular face.
Given, Height = 15 inch;
Base edge = 34 inch;
TSA =?
Here we use pythagoras theorem for the Right Triangle AOM, we get:
b2 = (15)2 + (17)2;
b2 = 225 + 289;
b = √ 514;
b = 22.67 inch;
Now we will find the Area of Triangle ASR;
Area of triangle ASR = ½ * b * h;
Area of triangle ASR = ½ * 34 * 22.67;
Area = ½ * 770.78;
Area = 385.39 inch2;
Now area of Square base = s2
Area = (34)2;
Area = 1156 inch2;
Now put these values in the formula and we will get TSA of pyramid.
TSA = area of the base + 4 * area of triangular face;
TSA = 385.39 + 4 * 1156;
TSA = 5009.39 inch2.
So the TSA of pyramid is 5009.39 inch2.

## Find the total surface area of a pyramid which has perpendicular height of 5.2 inch and base edge of 16 inch?

The formula for finding the total surface area of a pyramid = area of the base + 4 * area of triangular face.
Given, Height = 5.2 inch;
Base edge = 16 inch;
TSA =?
Here we use pythagoras theorem for the Right Triangle AOM, we get:
b2 = (5.2)2 + (8)2;
b2 = 27.04 + 64;
b = √ 91.04;
b = 9.54 inch;
Area of triangle ASR = ½ * b * h;
Area of triangle ASR = ½ * 16 * 9.54;
Area = 76.33 inch2;
Now area of Square base = s2
Area = (16)2;
Area = 256 inch2;
Now put these values in the formula and we will get TSA of pyramid.
TSA = area of the base + 4 * area of triangular face;
TSA = 256 + 4 * 76.33;
TSA = 561.32 inch2.
So the TSA of pyramid is 561.32 inch2.

## Find the total surface area of pyramid which has perpendicular height of 13 inch and base edge of 32 inch?

The formula for finding the total surface area of a pyramid = area of base + 4 * area of triangular face.

Given, Height = 13 inch;
Base edge = 32 inch;
TSA =?
Here we use pythagoras theorem for the Right Triangle AOM, we get:
b2 = (13)2 + (16)2;
b2 = 169 + 256;
b = √ 425;
b = 20.61 inch;
Now we will find the Area of Triangle ASR;
Area of triangle ASR = ½ * b * h;
Area of triangle ASR = ½ * 32 * 20.61;
Area = ½ * 659.52;
Area = 329.76 inch2;
Now area of Square base = s2
Area = (32)2;
Area = 1024 inch2;
Now put these values in the formula and we will get TSA of pyramid.
TSA = area of the base + 4 * area of triangular face;
TSA = 329.76 + 4 * 1024;
TSA = 4425.76 inch2.
So the TSA of pyramid is 4425.76 inch2.

## Find the total surface area of square pyramid which has perpendicular height of 18 inch and base edge of 30 inch?

The formula for finding the total surface area of a pyramid = area of base + 4 * area of triangular face.

Given, Height = 18 inch;
Base edge = 30 inch;
TSA =?
Here we use pythagoras theorem for the Right Triangle AOM, we get:
b2 = (18)2 + (15)2;
b2 = 324 + 225;
b = √ 549;
b = 23.43;
So length of ‘b’ is 23.43 inch;
Now we will find the Area of Triangle ASR;

Area of triangle ASR = ½ * b * h;
So value of ‘b’ is 30 and value of ‘h’ is 23.43;
Put these values in the above formula we get:
Area of triangle ASR = ½ * 30 * 23.43;
Area = ½ * 702.9;
Area = 351.45 inch2;
Now area of Square base = s2
Area = (30)2;
Area = 900 inch2;
Now put these values in the formula and we will get TSA of pyramid.
TSA = area of the base + 4 * area of triangular face;
TSA = 900 + 4 * 351.45;
TSA = 900 + 1405.8;
TSA = 2305.8 inch2.
So total surface area of pyramid is 2305.8 inch2.

## Find the volume of a rectangular based pyramid whose base is 25 inch and 22 inch and height is 15 inch?

Given, length = 25 inch and height = 22 inch;
Height = 15 inch;
Volume of a pyramid =?
The formula for finding the volume of a pyramid is given by:
Volume of a pyramid = 1/3 * A * h;
Or we can also write as:
Volume of a pyramid = 1/3 * l* w * h;
Where ‘l’ is length, ‘w’ is width and ‘h’ is the height of a pyramid.
On putting the values in the given formula then we get the volume of a pyramid.
Volume of a pyramid = 1/3 * l* w * h;
Volume = 1/3 * 25* 22 * 15;
Volume = 1/3 * 8250;
Volume = 8250/3;
Volume = 2750 inch3.
So the volume of a pyramid is 2750 inch3.

## Find the volume of rectangular based pyramid whose base is 16 inch and 11 inch and height is 9 inch?

Given, length = 16 inch and width = 11 inch;
Height = 9 inch;
Volume of a pyramid =?
The formula for finding the volume of a pyramid is given by:
Volume of a pyramid = 1/3 * A * h;
Or we can also write as:
Volume of a pyramid = 1/3 * l* w * h;
Where ‘l’ is length, ‘w’ is width and ‘h’ is the height of pyramid.
On putting the values in the given formula then we get the volume of a pyramid.
Volume of a pyramid = 1/3 * l* w * h;
Volume = 1/3 * 16 * 11 * 9;
Volume = 1/3 * 1584;
Volume = 1584/3;
Volume = 528 inch3.
So the Volume of Pyramid is 528 inch3.

## A pyramid has a square base of side 8 inch and volume of pyramid is 120 inch3, then find the height of a pyramid?

Given, base of side = 8 inch;
Volume of a pyramid = 120 inch3,
Height =?
The formula for finding the Volume of Pyramid is given by:
Volume of a pyramid = 1/3 * A * h;
Or we can also write as:
Volume of a pyramid = 1/3 * l2 * h;
Where ‘l’ is base of a side and ‘h’ is the height of a pyramid.
On putting the values in the given formula then we get the volume of a pyramid.
Volume of a pyramid = 1/3 * l2 * h;
120 = 1/3 * (8)2 * h;
120 = 1/3 * 64 * h;
120 = 21.33h;
h = 120/21.33 inch,
h = 5.62 inch.
So the height of a pyramid is 5.62 inch.

## Find the volume of a rectangular pyramid whose base is 13 inch and 10 inch and height is 7 inch?

Given, length = 13 inch and width = 10 inch;
Height = 7 inch;
Volume of a pyramid =?
The formula for finding the Volume of Pyramid is given by:
Volume of a pyramid = 1/3 * A * h;
Or we can also write as:
Volume of a pyramid = 1/3 * l* w * h;
Where ‘l’ is length, ‘w’ is width and ‘h’ is the height of pyramid.
On putting the values in the given formula then we get the volume of a pyramid.
Volume of a pyramid = 1/3 * l* w * h;
Volume = 1/3 * 13* 10 * 7;
Volume = 1/3 * 910;
Volume = 910/3;
Volume = 303.33 inch3.
So the volume of a pyramid is 303.33 inch3.

## A pyramid has a square base of side 6 inch and height of 10 inch. Find the volume of a pyramid?

Given, base of side = 6 inch;
Height = 10 inch;
Volume of pyramid =?
The formula for finding the volume of a pyramid is given by:
Volume of a pyramid = 1/3 * A * h;
Or we can also write as:
Volume of a pyramid = 1/3 * l2 * h;
Where ‘l’ is side of base and ‘h’ is the height of pyramid.
On putting the values in the given formula then we get the volume of a pyramid.
Volume of a pyramid = 1/3 * l2 * h;
Volume = 1/3 * (6)2 * 10;
Volume = 1/3 * 36 * 10;
Volume = 360/3;
Volume = 120 inch3.
So the volume of a pyramid is 120 inch3.
Math Topics
Top Scorers in Worksheets