Question

formula for surfacea area of rectangular pyramid

Answer 1

The surface area \( S \) of a rectangular pyramid can be calculated using the following formula:

\[
S = A_b + A_l
\]

Where:
- \( A_b \) is the area of the base (the rectangle).
- \( A_l \) is the total area of the four triangular faces (lateral surface area).

1. **Calculate the area of the base \( A_b \)**:
If the base has length \( l \) and width \( w \):
\[
A_b = l \times w
\]

2. **Calculate the lateral surface area \( A_l \)**:
- Let \( h \) be the height of the pyramid (the perpendicular height from the apex to the base) and \( s_1 \) and \( s_2 \) be the slant heights of the triangular faces:
- There are two triangles with base \( l \) and height \( s_1 \), and two triangles with base \( w \) and height \( s_2 \).

So the lateral area is given by:
\[
A_l = \frac{1}{2} \times l \times s_1 + \frac{1}{2} \times w \times s_2
\]

Therefore, the total surface area becomes:
\[
S = (l \times w) + \left(\frac{1}{2} \times l \times s_1 + \frac{1}{2} \times w \times s_2\right)
\]

This formula allows you to calculate the surface area of a rectangular pyramid using the base dimensions and the slant heights of the triangular faces.