Question

question 12 (multiple choice worth 2 points) (surface area of rectangular prisms and pyramids mc) a geologist has a rock that is shaped like a rectangular pyramid that she would like to give as a gift. a model of the rock is shown. image of a rectangular pyramid with labeled dimensions: 5.8 in, 6 in, 5 in, 4 in how much wrapping paper is needed without overlapping? options: 53 in², 73 in², 93 in², 146 in²

Explanation:

Step1: Find the area of the base

The base is a rectangle with length \( 5 \) in and width \( 4 \) in. The area of a rectangle is \( A = l \times w \), so \( A_{base} = 5 \times 4 = 20 \) \( \text{in}^2 \).

Step2: Find the area of the triangular faces

There are two pairs of triangular faces.

• For the triangles with base \( 5 \) in and height \( 6 \) in: The area of one such triangle is \( \frac{1}{2} \times 5 \times 6 = 15 \) \( \text{in}^2 \). There are two of these, so total area is \( 2 \times 15 = 30 \) \( \text{in}^2 \).
• For the triangles with base \( 4 \) in and height \( 5.8 \) in: The area of one such triangle is \( \frac{1}{2} \times 4 \times 5.8 = 11.6 \) \( \text{in}^2 \). There are two of these, so total area is \( 2 \times 11.6 = 23.2 \) \( \text{in}^2 \).

Step3: Find the total surface area

Add the area of the base and the areas of the triangular faces: \( \text{Total Surface Area} = 20 + 30 + 23.2 = 73.2 \approx 73 \) \( \text{in}^2 \).

Answer:

\( 73 \text{ in}^2 \) (corresponding to the option "73 in²")