Question

what is the surface area of this rectangular pyramid? 9.7 cm 9.1 cm 9.1 cm square centimeters submit

Explanation:

Step1: Identify the base and lateral faces

The base is a square with side length \( 9.1 \, \text{cm} \). The lateral faces are four congruent triangles with base \( 9.1 \, \text{cm} \) and slant height \( 9.7 \, \text{cm} \).

Step2: Calculate the area of the base

The area of the square base \( A_{\text{base}} = s^2 \), where \( s = 9.1 \, \text{cm} \).
\[
A_{\text{base}} = 9.1^2 = 82.81 \, \text{cm}^2
\]

Step3: Calculate the area of one lateral triangle

The area of a triangle \( A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{slant height} \).
\[
A_{\text{triangle}} = \frac{1}{2} \times 9.1 \times 9.7 = \frac{1}{2} \times 88.27 = 44.135 \, \text{cm}^2
\]

Step4: Calculate the total area of the four lateral triangles

\[
A_{\text{lateral}} = 4 \times 44.135 = 176.54 \, \text{cm}^2
\]

Step5: Calculate the total surface area

The total surface area \( A_{\text{total}} = A_{\text{base}} + A_{\text{lateral}} \).
\[
A_{\text{total}} = 82.81 + 176.54 = 259.35 \, \text{cm}^2
\]

Answer:

\( 259.35 \)