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Cross Sections Test Answer Key with Scoring – Grade 7

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

Grade 7 Math Test Answer Keys – Mathbot, the Math Made Easy robot coach, with free printable test answer keys for Grade 7
Looking for a cross sections test answer key? Then this answer key gives the solutions and the scoring guide of the Grade 7 test on Cross Sections of Prisms and Pyramids. Award points as marked. Accept any correct description in Question 8, and award the area point whenever the dimensions are used correctly, even if an earlier dimension was wrong and the multiplication is correct.

Standards: 7.G.A.3 · Level: Grade 7

Question 1 Name the Cross Sections (2 points)

  1. A rectangle (the same size as the base).
  2. A triangle.

Scoring: 1 point per part.

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

  1. A trapezoid.
  2. The apex is not on the plane, so the slice does not come to a point. It keeps two parallel sides, one lower and one shorter, joined by two slanted sides.

Scoring: 1 point per part.

Question 3 Vertical Cut of a Prism (3 points)

  1. A rectangle.
  2. It copies the 9-by-7 face: 9 in by 7 in.
  3. 9 × 7 = 63 square inches.
9 in7 in
The cross section: a 9 in by 7 in rectangle.

Scoring: 1 point per part.

Question 4 Parallel Cut of a Pyramid (3 points)

  1. A rectangle, similar to the base.
  2. Scale factor: 5 ÷ 10 = 12. Dimensions: 14 × 12 = 7 and 8 × 12 = 4, so 7 in by 4 in.
  3. 7 × 4 = 28 square inches.
7 in4 in
The cross section: 7 in by 4 in.

Scoring: 1 point per part.

Question 5 Triangle Through the Apex (2 points)

The triangle has base 14 in and height 10 in. Area: 12 × 14 × 10 = 70.

Base 14 in, height 10 in; 70 square inches

Scoring: 1 point for the dimensions, 1 point for the area.

Question 6 Square or Not? (3 points)

  1. It copies the base: 6 in by 6 in.
  2. One side is the height 11 in and the other is 6 in: 6 in by 11 in.
  3. Only the cross section parallel to the base is a square, because its sides are equal (6 = 6), while 6 ≠ 11.

Scoring: 1 point per part.

Question 7 Fish Tank (3 points)

  1. 30 × 12 = 360 square inches.
  2. 360 × 10 = 3,600 cubic inches.
  3. 30 × 10 = 300 square inches.

Scoring: 1 point per part.

Question 8 Find the Flaw (2 points)

  1. A plane parallel to the base cuts the pyramid at some height.
  2. The cross section is a rectangle, smaller than the base. (A vertical cut missing the apex, a trapezoid, is also accepted.)

Scoring: 1 point per part.

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