Total Surface Area of Square Pyramid given Slant Height and Height Calculator

Total Surface Area of Square Pyramid Formula:

\[ TSA = (4 \times (h_{slant}^2 - h^2)) + (4 \times h_{slant} \times \sqrt{h_{slant}^2 - h^2}) \]

Total Surface Area of Square Pyramid:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Total Surface Area of Square Pyramid?

The Total Surface Area of Square Pyramid is the total amount of two-dimensional space occupied on all the faces of the Square Pyramid, including the base and the four triangular faces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = (4 \times (h_{slant}^2 - h^2)) + (4 \times h_{slant} \times \sqrt{h_{slant}^2 - h^2}) \]

Where:

\( TSA \) — Total Surface Area of Square Pyramid (m²)
\( h_{slant} \) — Slant Height of Square Pyramid (m)
\( h \) — Height of Square Pyramid (m)

Explanation: The formula calculates the total surface area by summing the area of the square base and the areas of the four triangular faces.

3. Importance of Surface Area Calculation

Details: Calculating the total surface area is important in various applications such as construction, packaging, material estimation, and geometric analysis of pyramid structures.

4. Using the Calculator

Tips: Enter the slant height and height of the square pyramid in meters. Both values must be positive, and the slant height must be greater than the height for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between slant height and height?
A: The height is the perpendicular distance from the apex to the base, while the slant height is the distance along the lateral face from the apex to the midpoint of a base edge.

Q2: Why must slant height be greater than height?
A: This is a geometric constraint - in any right square pyramid, the slant height must always be greater than the perpendicular height.

Q3: Can this formula be used for oblique square pyramids?
A: No, this formula is specifically for right square pyramids where the apex is directly above the center of the base.

Q4: What units should I use for the inputs?
A: The calculator accepts inputs in meters, but the formula works with any consistent unit of length.

Q5: How accurate is the calculation?
A: The calculation provides results with 6 decimal places precision, suitable for most engineering and mathematical applications.