Math Examples of Pyramids

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 inch^2;
So LSA of triangular pyramid is 214.5 inch².

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 inch^2;
So LSA of a triangular pyramid is 408 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.

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.

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.

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.

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.

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.

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.

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_.

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.

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.

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.

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.

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.