This grade 7 cross test answer key gives the full solution and the scoring guide for each of the 8 test questions on cross sections of 3d figures.
This answer key for the cross sections test shows a worked solution for every question, together with a scoring guide that explains how the 20 points are awarded. Give partial credit when the shape is named correctly even if a later dimension or area has an arithmetic slip.
Grade 7 Cross Test Answer Key: questions 1–5
Question 1: Name the cross section (2 points)
- Rectangle
- Triangle
Scoring: 1 point per part.
Question 2: Vertical slice of a prism (3 points)
- A rectangle 5 in. by 6 in.
- \(5\times 6=30\): \(30\text{ in.}^{2}\)
Scoring: part (a) 1 point for rectangle and 1 point for both dimensions. Part (b) 1 point.
Question 3: Pyramid sliced parallel to the base (3 points)
- The slice is a rectangle. Halfway up, each side is half the base side: \(14: 2=7\) and \(10: 2=5\). Rectangle 7 in. by 5 in.
- \(7\times 5=35\): \(35\text{ in.}^{2}\)
Scoring: part (a) 1 point for rectangle and 1 point for both dimensions. Part (b) 1 point.
Question 4: Slice through the apex (2 points)
- Triangle
- The base of the triangle is 9 ft and its height is 12 ft. \(\frac{1}{2}\times 9\times 12=54\): \(54\text{ ft}^{2}\)
Scoring: 1 point per part.
Question 5: Trapezoid cross section (3 points)
- Trapezoid
- \(A=\frac{1}{2}(8+4)\times 4.5=6\times 4.5=27\): \(27\text{ ft}^{2}\)
Scoring: part (a) 1 point. Part (b) 1 point for using \(\frac{1}{2}(b_1+b_2)h\) correctly and 1 point for the answer 27 with square feet.
Grade 7 Cross Test Answer Key: questions 6–8
Question 6: Triangle claim (2 points)
No. Every face of a rectangular prism is a rectangle, and a plane perpendicular to the base meets the prism in a rectangle whose height is the height of the prism. A triangle cannot be formed.
Scoring: 1 point for answering no. 1 point for an explanation that the cross section is always a rectangle.
Question 7: Slice across a diagonal (3 points)
- Rectangle
- The length is the base diagonal, 10 in., and the width is the height, 7 in. \(10\times 7=70\): 10 in. by 7 in., area \(70\text{ in.}^{2}\)
Scoring: part (a) 1 point. Part (b) 1 point for both dimensions and 1 point for the area.
Question 8: Block of clay (2 points)
- A rectangle 9 in. by 4 in., the same size as the base.
- The bottom piece is a prism 9 in. by 4 in. by 1 in. \(9\times 4\times 1=36\): \(36\text{ in.}^{3}\)
Scoring: 1 point per part.
Scoring summary
20 points: add the points of every question of this grade 7 cross test answer key.
How to use this grade 7 cross test answer key
Use this grade 7 cross test answer key to score the test fairly and to see which skills need more practice.
See every chapter on the Grade 7 math page.