For Exercises 18-21, use the following information. This...

For Exercises $18-21$, use the following information. This solid is a composite of a cube and square pyramid. The base of the solid is the base of the cube. Find the indicated measurements for the solid. Which has the greater lateral area: the pyramid or the cube? Explain. (GRAPH CANT COPY)

For Exercises $18-21$, use the following information. This solid is a composite of a cube and square pyramid. The base of the solid is the base of the cube. Find the indicated measurements for the solid.
Which has the greater lateral area: the pyramid or the cube? Explain.
(GRAPH CANT COPY)

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Key Concepts

Square Pyramid

A square pyramid is a polyhedron with a square base and four triangular lateral faces that connect at a common apex. The lateral surface area of a square pyramid is determined by calculating the area of one of its congruent triangles and multiplying by four. This concept is fundamental when analyzing and comparing the surface areas of composite solids.

Composite Solids

Composite solids are figures made by combining two or more simple solids. In problems involving composite solids, it is important to break down the solid into its constituent parts, calculate measurements such as surface area or volume for each part, and then compare or combine them as required.

Lateral Surface Area

Lateral surface area is the area of all the sides of a solid excluding its base(s). It is a key measurement in comparing different parts of three-dimensional figures, such as the sides of a cube versus the triangular faces of a pyramid.

Cube

A cube is a regular hexahedron with six identical square faces. When focusing on lateral surface area, one considers the four vertical faces that surround the cube's base. Understanding the properties of a cube, such as equal edge lengths and symmetric faces, is crucial for calculating and comparing its areas.

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