Question

thought provoking you are designing the living - room of an apartment. counting the floor, walls, and ceiling you want the design to contain at least eight different planes. which design(s) satisfy this requirement? four rectangle walls at right angles, flat floor, flat ceiling; six square walls arranged around the edge of a regular hexagon, flat floor, flat ceiling; a pyramid - shaped room with square floor and four triangular walls that meet at a vertex; a room with a pentagon - shaped floor, five rectangular walls, and a ceiling that forms the lateral faces of a pentagonal pyramid; a room in the form of a pentagonal prism

Explanation:

Step1: Count planes in first option

Four walls, one floor, one ceiling gives 4 + 1+ 1 = 6 planes.

Step2: Count planes in second option

Six walls, one floor, one ceiling gives 6 + 1 + 1=8 planes.

Step3: Count planes in third option

One floor, four walls gives 1 + 4 = 5 planes.

Step4: Count planes in fourth option

One floor, five walls, one ceiling gives 1+5 + 1 = 7 planes.

Step5: Count planes in fifth option

Two bases (top - ceiling and bottom - floor) and five lateral faces of prism gives 2+5 = 7 planes.

Answer:

B. Six square walls arranged around the edge of a regular hexagon, flat floor, flat ceiling