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Cross Sections Test – Grade 7 Math (Printable PDF)

Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

Grade 7 Math Tests – Mathbot, the Math Made Easy robot coach, with free printable tests for Grade 7
Looking for a cross sections test? Then this Grade 7 test on Cross Sections of Prisms and Pyramids checks the whole chapter, with points for each question. This test covers cross sections of rectangular prisms and pyramids cut by planes parallel or perpendicular to the base: naming shapes, finding dimensions and computing areas. Sketch the plane when it helps. Calculators are not allowed. Plan on 45 minutes for the 8 questions.

Standards: 7.G.A.3 · Level: Grade 7

Time: 45 minutes · 8 questions · Total: 20 points · Calculator: as allowed by your teacher

Question 1 Name the Cross Sections (2 points)

Name the shape of each cross section.

  1. A rectangular prism cut parallel to its base (1 point)
  2. A rectangular pyramid cut by a vertical plane through its apex (1 point)

Question 2 A Slice That Misses the Apex (2 points)

An upright flat cut slices a pyramid but misses the apex.

  1. Name the cross section. (1 point)
  2. Explain why it is not a triangle. (1 point)

Question 3 Vertical Cut of a Prism (3 points)

A prism is cut as shown.

9 in4 in7 in
Vertical cut parallel to the 9-by-7 face.
  1. Name the cross section. (1 point)
  2. Give its dimensions. (1 point)
  3. Find its area. (1 point)

Question 4 Parallel Cut of a Pyramid (3 points)

The pyramid is cut by a plane parallel to its base, 5 in below the apex.

14 in8 in10 in
Cut 5 in below the apex.
  1. Name the cross section. (1 point)
  2. Find its dimensions. (1 point)
  3. Find its area. (1 point)

Question 5 Triangle Through the Apex (2 points)

For the pyramid in Question 4, a vertical plane through the apex is parallel to the 14 in base edges. Find the dimensions and the area of the cross section.

Question 6 Square or Not? (3 points)

A box-shaped prism has a 6 in by 6 in bottom and stands 11 in tall.

  1. Find the dimensions of a cross section parallel to the base. (1 point)
  2. Find the dimensions of a cross section perpendicular to the base. (1 point)
  3. Which of these cross sections is a square? Explain. (1 point)

Question 7 Fish Tank (3 points)

A fish tank measures 30 in by 12 in by 15 in. It contains water 10 in deep.

  1. Find the area of the water’s surface. (1 point)
  2. Find the volume of the water. (1 point)
  3. Find the area of the wet part of a vertical cross section parallel to the 30-by-15 face. (1 point)

Question 8 Find the Flaw (2 points)

Dana says, “Every cross section of a pyramid is a triangle.”

  1. Describe a cut of a rectangular pyramid that is not a triangle. (1 point)
  2. Name the shape of that cross section. (1 point)

View the Cross Sections test answer key with scoring

Cross Sections lessonCross Sections worksheetCross Sections quiz