Question

what is the surface area of this rectangular pyramid?
image of a rectangular pyramid with base sides 7 cm, 7 cm and a triangular face height 9 cm
square centimeters
submit

Explanation:

Step1: Identify the base and lateral faces

The base is a square with side length \( 7 \, \text{cm} \). The lateral faces are four congruent triangles with base \( 7 \, \text{cm} \) and slant height \( 9 \, \text{cm} \).

Step2: Calculate the area of the base

The area of the square base is \( \text{side}^2 \), so:
\[
\text{Base Area} = 7 \times 7 = 49 \, \text{cm}^2
\]

Step3: Calculate the area of one lateral triangle

The area of a triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \) (here, height is the slant height). For one triangle:
\[
\text{Area of one triangle} = \frac{1}{2} \times 7 \times 9 = 31.5 \, \text{cm}^2
\]

Step4: Calculate the total area of the four lateral triangles

Since there are four congruent triangles:
\[
\text{Total Lateral Area} = 4 \times 31.5 = 126 \, \text{cm}^2
\]

Step5: Calculate the total surface area

Add the base area and the total lateral area:
\[
\text{Surface Area} = 49 + 126 = 175 \, \text{cm}^2
\]

Answer:

\( 175 \)