Cross Sections of 3D Figures: Grade 7 Math Test Answer Key – PDF Download

Question 1: Name the cross section (2 points)

1. Rectangle
2. Triangle

Scoring: 1 point per part.

Question 2: Vertical slice of a prism (3 points)

1. A rectangle 5 in. by 6 in.
2. \(5\times 6=30\): \(30\text{ in.}^{2}\)

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)

1. 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.
2. \(7\times 5=35\): \(35\text{ in.}^{2}\)

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)

1. Triangle
2. 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)

1. Trapezoid
2. \(A=\frac{1}{2}(8+4)\times 4.5=6\times 4.5=27\): \(27\text{ ft}^{2}\)

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.

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)

1. Rectangle
2. 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)

1. A rectangle 9 in. by 4 in., the same size as the base.
2. 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.

⬇ Download the Grade 7 Cross Sections of 3D Figures test answer key (PDF, 87 KB)

See every chapter on the Grade 7 math page.