Question

practice
paul unfolded a pyramid container and wanted to determine the area of entire container. what is the area in ft²?
a. 16 ft²
b. 6 ft²
c. 12 ft²
d. 28 ft²
when the base shape is a square, your triangles will always be isosceles triangles.
houston independent school district

Explanation:

Step1: Calculate area of square base

The base is a square with side length \( 4 \, \text{ft} \). The area of a square is \( \text{side}^2 \), so \( 4 \times 4 = 16 \, \text{ft}^2 \).

Step2: Calculate area of one triangular face

Each triangular face has a base of \( 4 \, \text{ft} \) and a height of \( 1.5 \, \text{ft} \). The area of a triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \), so \( \frac{1}{2} \times 4 \times 1.5 = 3 \, \text{ft}^2 \).

Step3: Calculate total area of triangular faces

There are 4 triangular faces, so total area of triangles is \( 4 \times 3 = 12 \, \text{ft}^2 \).

Step4: Calculate total surface area

Add the area of the base and the total area of the triangles: \( 16 + 12 = 28 \, \text{ft}^2 \).

Answer:

D. \( 28 \, \text{ft}^2 \)