Question

what is the surface area of this rectangular pyramid? 2 cm 2 cm 3 cm square centimeters submit

Explanation:

Step1: Identify the base and lateral faces

The base is a square with side length \( 2 \, \text{cm} \). The lateral faces are four congruent triangles. The base of each triangle is \( 2 \, \text{cm} \) and the height (slant height) is \( 3 \, \text{cm} \).

Step2: Calculate the area of the base

The area of the square base \( A_{\text{base}} \) is given by the formula \( A = s^2 \), where \( s = 2 \, \text{cm} \).
\[
A_{\text{base}} = 2^2 = 4 \, \text{cm}^2
\]

Step3: Calculate the area of one lateral triangle

The area of a triangle is \( A = \frac{1}{2} \times \text{base} \times \text{height} \). For one lateral triangle, base \( = 2 \, \text{cm} \) and height \( = 3 \, \text{cm} \).
\[
A_{\text{lateral triangle}} = \frac{1}{2} \times 2 \times 3 = 3 \, \text{cm}^2
\]

Step4: Calculate the total area of the four lateral triangles

Since there are four congruent lateral triangles, the total lateral surface area \( A_{\text{lateral}} \) is:
\[
A_{\text{lateral}} = 4 \times 3 = 12 \, \text{cm}^2
\]

Step5: Calculate the total surface area

The total surface area \( A_{\text{total}} \) is the sum of the base area and the lateral surface area.
\[
A_{\text{total}} = A_{\text{base}} + A_{\text{lateral}} = 4 + 12 = 16 \, \text{cm}^2
\]

Answer:

\( 16 \)