The surface area, or total surface area (TSA), of a square pyramid, is the entire space occupied by its five flat faces. It is measured in square units such as m2, cm2, mm2, and in2.
Formula
The formula to calculate the surface area of a square pyramid also includes its lateral surface area (LSA). The formula is:
Surface Area of a Square Pyramid
Lateral Surface Area (LSA) = 2bs, here b = base, s = slant height
∴ Total Surface Area(TSA) = b2 + LSA
Let us solve some examples to understand the concept better.
Solved Examples
Find the lateral and total surface area for a square pyramid with a base of 7 cm, and a slant height of 12 cm.
Solution:
As we know, Lateral Surface Area (LSA) = 2bs, here b = 7 cm, s = 12 cm ∴ LSA = 2 × 7 × 12 = 168 cm2 Total Surface Area (TSA) = b2 + LSA, here b = 7 cm, LSA = 168 cm2 ∴ TSA =72 + 168 = 217 cm2
Finding the lateral surface area for a square pyramid when BASE and HEIGHT are known
Find the lateral surface area for a square pyramid with a base of 4 cm, and a height of 6 cm.
Solution:
We will use an alternative formula here. Lateral Surface Area (LSA) = ${b\sqrt{b^{2}+4h^{2}}}$, here b = 4 cm, h = 6 cm ∴ LSA = ${4\sqrt{4^{2}+4\times 6^{2}}}$ = 50.6 cm2
Find the total surface area for a square based pyramid with a base of 8 cm, and a slant height of 18 cm.
Solution:
As we know, Total Surface Area (TSA) = b2 + 2bs, here b = 8 cm, s = 18 cm ∴ TSA = 82+ 2 × 8 × 18 = 352 cm2
Finding the total surface area for a square pyramid when BASE and HEIGHT are known
Find the total surface area for a square pyramid with a base of 3 cm, and a height of 13 cm.
Solution:
Here, we will use an alternative formula. Total Surface Area (TSA) = ${b^{2}+b\sqrt{b^{2}+4h^{2}}}$, here b = 3 cm, h = 13 cm ∴ TSA = ${3^{2}+3\sqrt{3^{2}+4\times 13^{2}}}$ = 87.51 cm2
