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7th Grade Math

Examples, solutions, videos, and worksheets to help grade 7 students describe rectangular regions that result from slicing a right rectangular prism by a plane perpendicular to one of the faces and describe polygonal regions that result from slicing a right rectangular pyramid by a plane perpendicular to the base and by another plane parallel to the base.

Printable “Solid Shapes” Worksheets:

Nets of Solid Figures

Find Surface Area using Nets

Volume of Rectangular Prisms

Volume of Composite Rectangular Prisms

Slicing Solids

**Slicing Rectangular Prism**

A rectangular prism is a three-dimensional solid with six faces, where each face is a rectangle. The faces are paired, with opposite faces being congruent. A rectangular prism has three dimensions: length (l), width (w), and height (h).

Slicing a rectangular prism refers to cutting the prism along a plane, resulting in a cross-section. The shape of the cross-section depends on the orientation and position of the slice relative to the prism.

Types of Slices in a Rectangular Prism

Horizontal Slice (Parallel to the Base):

The cross-section will be a rectangle that has the same length and width as the base of the prism.

Vertical Slice (Perpendicular to the Base):

If you slice the prism vertically along a plane parallel to one of the sides, the cross-section will be a rectangle.

**Slicing Square-based Pyramid**

A square-based pyramid is a three-dimensional solid with a square base and four triangular faces that converge at a single point called the apex. The apex is directly above the center of the square base.

Slicing a square-based pyramid refers to cutting the pyramid along a plane, which results in a cross-section. The shape of the cross-section depends on the orientation and position of the slice relative to the pyramid.

Types of Slices in a Square-Based Pyramid

Horizontal Slice (Parallel to the Base):

The cross-section will be a smaller square. The size of this square depends on the height at which the slice is made. The closer the slice is to the base, the larger the square; the closer the slice is to the apex, the smaller the square.

Vertical Slice (Through the Apex):

If the slice passes through the apex and is vertical (perpendicular to the base), the cross-section will be an isosceles triangle. The base of this triangle will be a side of the square base, and the two other sides will correspond to two of the triangular faces of the pyramid.

Vertical Slice (Not Through the Apex):

If the slice is vertical but does not pass through the apex, the cross-section can be a trapezoid. The trapezoid is formed because the slice cuts through two of the triangular faces, creating two parallel sides of different lengths.

Have a look at this video if you need to review how to slice solids.

Click on the following worksheet to get a printable pdf document.

Scroll down the page for more **Slicing Solids Worksheets**.

**Printable**

(Answers on the second page.)

Slicing Solids Worksheet #1 (rectangular prisms)

Slicing Solids Worksheet #2 (rectangular prisms)

Slicing Solids Worksheet #3 (square-based pyramids)

Slicing a Rectangular Prism

Slicing a Pyramid

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