Examples on Surface Area of a Square Pyramid Formulas

Example 1: Calculate the total surface area of a square pyramid if its base is 10 cm and its slant height is 13 cm.

Solution:

We have,

a = 10

l = 13

Using the formula we have,

TSA = a² + 2al

= (10 × 10) + (2 × 10 × 13)

= 100 + 260

= 360 sq. cm

Example 2: Calculate the total surface area of a square pyramid if its base is 6 cm and its slant height is 8.54 cm.

Solution:

We have,

a = 6

l = 8.54

Using the formula we have,

TSA = a² + 2al

= (6 × 6) + (2 × 6 × 8.54)

= 36 + 102.53

= 138.53 sq. cm

Example 3: Calculate the total surface area of a square pyramid if its base is 11 cm and height is 9 cm.

Solution:

We have,

a = 11

h = 9

Using the formula we have,

TSA = a² + 2a√(a²/4 + h²)

= (11 × 11) + (2 × 11 √(11²/4 + 9²))

= 121 + 232.05

= 353.05 sq. cm

Example 4: Calculate the total surface area of a square pyramid if its base is 14 cm and height is 10 cm.

Solution:

We have,

a = 14

h = 10

Using the formula we have,

TSA = a² + 2a√(a²/4 + h²)

= (14 × 14) + (2 × 14 √(14²/4 + 10²))

= 196 + 341.8

= 537.8 sq. cm

Example 5: Calculate the lateral surface area of a square pyramid if its base is 3 cm and slant height is 4.27 cm.

Solution:

We have,

a = 3

l = 4.27

Using the formula we have,

LSA = 2al

= 2 × 13 × 4.27

= 25.63 sq. cm

Example 6: Calculate the lateral surface area of a square pyramid if its base is 13 cm and height is 10 cm.

Solution:

We have,

a = 13

h = 10

Using the formula we have,

LSA = 2a√(a²/4 + h²)

= 2 × 13 √(13²/4 + 10²)

= 310.1 sq. cm

Example 7: Calculate the lateral surface area of a square pyramid if its base is 9 cm and height is 14 cm.

Solution:

We have,

a = 9

h = 14

Using the formula we have,

LSA = 2a√(a²/4 + h²)

= 2 × 9 √(9²/4 + 14²)

= 264.7 sq. cm

Area of the square pyramid can be easily calculated using various formulas that are added in the article below. In this article, we have covered Square Pyramid definition, its formulas, examples and others in detail.