Question

1. find the surface area of the solid shown. it is composed of a cube and a right square pyramid.

Explanation:

Step1: Calculate cube's total surface area

The cube has 6 faces, each with area $6 \times 6$.
Expression: $6 \times (6^2) = 6 \times 36 = 216$ in²

Step2: Adjust cube's exposed area

Subtract the 1 face covered by the pyramid:
Expression: $216 - 36 = 180$ in²

Step3: Calculate 1 pyramid triangular face area

Each triangular face has base 6 in, height 4 in.
Expression: $\frac{1}{2} \times 6 \times 4 = 12$ in²

Step4: Calculate total pyramid lateral area

There are 4 identical triangular faces:
Expression: $4 \times 12 = 48$ in²

Step5: Sum all exposed surface areas

Add adjusted cube area and pyramid lateral area:
Expression: $180 + 48 = 264$ in²

Answer:

264 square inches