Rectangular Pyramid Surface Area Calculator

Base Length (a):

Base Width (b):

Height (H):

Base Diagonal (d, cm): Base Diagonal (d, m): Base Diagonal (d, in): Base Diagonal (d, ft):

Base Surface Area (A_b, cm²): Base Surface Area (A_b, m²): Base Surface Area (A_b, mm²): Base Surface Area (A_b, in²): Base Surface Area (A_b, ft²):

Lateral Surface Area (A_l, cm²): Lateral Surface Area (A_l, m²): Lateral Surface Area (A_l, mm²): Lateral Surface Area (A_l, in²): Lateral Surface Area (A_l, ft²):

Total Surface Area (A_t, cm²): Total Surface Area (A_t, m²): Total Surface Area (A_t, mm²): Total Surface Area (A_t, in²): Total Surface Area (A_t, ft²):

1. What is a Rectangular Pyramid Surface Area Calculator?

Definition: This calculator computes the base diagonal, base surface area (\( A_b \)), lateral surface area (\( A_l \)), and total surface area (\( A_t \)) of a rectangular pyramid using its base length (a), base width (b), and height (H).

Purpose: Useful for geometry, architecture, and design applications, such as calculating material needs for constructing or coating a rectangular pyramid.

2. How Does the Calculator Work?

Formulas:

Base Surface Area (\( A_b \)): \( A_b = a \times b \)
Slant Heights: \( l_a = \sqrt{h^2 + \left(\frac{b}{2}\right)^2} \), \( l_b = \sqrt{h^2 + \left(\frac{a}{2}\right)^2} \)
Lateral Surface Area (\( A_l \)): \( A_l = a \times l_a + b \times l_b \)
Total Surface Area (\( A_t \)): \( A_t = A_b + A_l \)
Base Diagonal (d): \( d = \sqrt{a^2 + b^2} \)

Explanation: Inputs are converted to meters, and the base diagonal, base area, lateral surface area, and total surface area are calculated. Results are converted to cm, m, in, ft for diagonals, and cm², m², mm², in², ft² for areas.

3. Importance of Rectangular Pyramid Calculations

Details: Essential for determining material requirements (e.g., paint or covering) and structural analysis in rectangular pyramid designs.

4. Using the Calculator

Tips: Enter base length (a), base width (b), and height (H) in units (mm, cm, m, in, ft; >0). Results include base diagonal (d) in cm, m, in, ft, and base area (\( A_b \)), lateral surface area (\( A_l \)), and total surface area (\( A_t \)) in cm², m², mm², in², ft².