Cross Sections of Prisms and Pyramids

Estimation What are the dimensions of the vertical cross section that is parallel to the right and left faces of the right rectangular​ prism? Note that the figure is not drawn to scale.

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The horizontal cross section shown is parallel to the base of the pyramid. If the shortest side of the cross section measures 1.2​ cm, what is the measure of the cross​ section's longest​ side? Explain.

• 2.4

• 0.6

• 8.4

• 7.2

A right rectangular prism has length 104 in. and width 66 in. The prism is 54 in. tall. What are the dimensions of a horizontal cross section of the​ prism? Use pencil and paper.

• 66 in.×104 in.

• 54 in.×66 in.

• 54 in.×104 in.

What is a good description of the cross section shown that is parallel to the edge of the pyramid that measures 5​ millimeters?

• Triangle with base of 5 and height of 16

• Triangle with base of 16 and height of 5

• Pyramid with base of 5 and height of 16

• Pyramid with base of 16 and height of 5

The base of a right rectangular pyramid has length 9 ​cm, width 3 ​cm, and height 18 cm. Describe a cross section that could be formed by a plane parallel to the base of the pyramid intersects the pyramid between its base and the vertex opposite its base.

• An equilateral triangle with base length and height forming the same​ ratio, 3:1, as the sides of the base. 

• An isosceles triangle with base length and height forming the same​ ratio, 3:1, as the sides of the base.

• A larger rectangle whose length and width form the same​ ratio, 3:1, as the sides of the base.

• A smaller rectangle whose length and width form the same​ ratio, 3:1, as the sides of the base. 

Describe a cross section formed by a vertical plane that intersects the front face and the vertex of the pyramid shown. The figure is not drawn to scale.

• An isosceles triangle with base length equal to the width of the base and height equal to the height of the pyramid.

• An isosceles triangle with base length equal to the width of the base and height less than the height of the pyramid.

• A rectangle with length and width equal to the length and width of the base of the pyramid.

• An equilateral triangle with base length equal to the width of the base and height less than the height of the pyramid.

A 0.75​-in.-thick slice is cut from a stick of butter as shown. What is the Area of the cross​ section? Note that the figure is not drawn to scale. Use pencil and paper.

• .75

• 1.5

• 3.19

• 4.25

What is the best way to slice the figure shown so that you have two identical​ pieces? Find the area of the cross section. Note that the figure is not drawn to scale.

• 81

• 126

• 63

• 25

Find the dimensions of the horizontal cross section of the right rectangular prism. Note that the figure is not drawn to scale.

• 1 x 5

• 1 x 12

• 5 x 12

The figure is not drawn to scale. Use pencil and paper.

Draw the cross section formed by the following plane. A horizontal plane above the base that intersects the faces of the pyramid shown.

• A rectangle with length and width equal to the length and width of the base.

• A rectangle with length and width less than the length and width of the base.

• A triangle with base and height less than the length and height of the pyramid.

• A triangle with base and height equal than the length and height of the pyramid.