Question

a rectangular pyramid is shown below.
which diagram is a net for this pyramid?
what is the surface area of the rectangular pyramid?
square square millimeters

Explanation:

Step1: Identify the base and lateral faces

The rectangular pyramid has a rectangular base with length \( l = 18 \) mm and width \( w = 10 \) mm, and four triangular lateral faces. Two pairs of congruent triangles: two triangles with base \( 18 \) mm and height \( 13 \) mm, and two triangles with base \( 10 \) mm and height \( 15 \) mm.

Step2: Calculate the area of the base

The area of the rectangular base \( A_{base} = l \times w = 18 \times 10 = 180 \) square millimeters.

Step3: Calculate the area of the first pair of triangular faces

Each triangle with base \( 18 \) mm and height \( 13 \) mm has area \( \frac{1}{2} \times 18 \times 13 \). For two such triangles, the total area \( A_1 = 2 \times \frac{1}{2} \times 18 \times 13 = 18 \times 13 = 234 \) square millimeters.

Step4: Calculate the area of the second pair of triangular faces

Each triangle with base \( 10 \) mm and height \( 15 \) mm has area \( \frac{1}{2} \times 10 \times 15 \). For two such triangles, the total area \( A_2 = 2 \times \frac{1}{2} \times 10 \times 15 = 10 \times 15 = 150 \) square millimeters.

Step5: Calculate the total surface area

The total surface area \( SA = A_{base} + A_1 + A_2 = 180 + 234 + 150 \).

\[
SA = 180 + 234 + 150 = 564
\]

Answer:

564