← Back to the Cross Sections worksheet
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: 7.G.A.3 · Level: Grade 7
Problem 1 Slice a Prism Flat
A prism has the same dimensions at every height, so the slice copies the base.
A rectangle
Problem 2 Slice a Pyramid Flat
Each parallel slice of a rectangular pyramid has four right angles but is smaller than the base.
A rectangle (smaller than the base)
Problem 3 Stand the Plane Up
The slice has the prism’s height as one side and a base edge as the other, with four right angles.
A rectangle
Problem 4 Through the Apex
The slice runs from two base points up to the apex.
A triangle
Problem 5 Prism Parallel Slice Area
The slice copies the base: 8 in by 5 in. Area: 8 × 5 = 40.
8 in by 5 in; 40 square inches
Problem 6 Gift Box Vertical Slice
The cut copies the 12-by-4 face. Area: 12 × 4 = 48.
12 in by 4 in; 48 square inches
Problem 7 Cereal Box Slice
The slice is 2.5 in by 10 in. Area: 2.5 × 10 = 25.
25 square inches
Problem 8 Halfway Up the Pyramid
Scale factor: 6 ÷ 12 = 12. Dimensions: 10 × 12 = 5 and 6 × 12 = 3. Area: 5 × 3 = 15.
5 in by 3 in; 15 square inches
Problem 9 Near the Top
Scale factor: 3 ÷ 12 = 14. Dimensions: 10 × 14 = 2.5 and 6 × 14 = 1.5. Area: 2.5 × 1.5 = 3.75.
2.5 in by 1.5 in; 3.75 square inches
Problem 10 Triangle Along the Length
The base of the triangle is the base length 10 in, and its height is the pyramid height 12 in. Area: 12 × 10 × 12 = 60.
Base 10 in, height 12 in; 60 square inches
Problem 11 Triangle Across the Width
The triangle has base 6 in and height 12 in. Area: 12 × 6 × 12 = 36.
Base 6 in, height 12 in; 36 square inches
Problem 12 Match the Slice
(a) The slice has four right angles: rectangle. (b) Two base points meet at the apex: triangle. (c) The cut removes the tip, leaving two parallel sides: trapezoid. (d) Smaller copy of the base: rectangle.
(a) rectangle, (b) triangle, (c) trapezoid, (d) rectangle
Problem 13 A Trapezoid Slice
Area of a trapezoid = 12(b1 + b2)h = 12(12 + 9)(3) = 12 × 21 × 3 = 31.5.
31.5 square inches
Problem 14 When Is the Slice a Square?
A cut parallel to the base copies the base: 6 in by 6 in, a square. A cut perpendicular to the base has the height 10 in as one side and 6 in as the other, so it is a 6-by-10 rectangle, not a square.
Only cuts parallel to the base: 6 in by 6 in squares
Problem 15 Slicing a Bread Loaf
The cut is perpendicular to the length, so the cross section is 4 in by 4 in: a square with area 16 sq in. Slices: 14 ÷ 0.5 = 28.
A square of 16 square inches; 28 slices
Problem 16 Glass Museum Floor
The floor is 18 − 9 = 9 ft below the apex, so the scale factor is 9 ÷ 18 = 12. Dimensions: 12 ft by 8 ft. Area: 96.
12 ft by 8 ft; 96 square feet
Problem 17 Two Tent Triangles
First triangle: 12 × 10 × 6 = 30. Second triangle: 12 × 8 × 6 = 24. Difference: 30 − 24 = 6.
The first triangle, by 6 square feet
Problem 18 Aquarium Water Level
The water surface is parallel to the base: 40 × 16 = 640 sq in. The wet cross section is 40 by 12: 480 sq in. Volume: base area × depth = 640 × 12 = 7,680.
640 sq in; 480 sq in; 7,680 cubic inches
Problem 19 Two Cuts in a Concrete Block
Cut 1: 18 × 8 = 144 sq in. Cut 2: 18 × 6 = 108 sq in. Difference: 144 − 108 = 36.
Cut 1, by 36 square inches
Problem 20 Glass Paperweight
4 cm below the apex: scale 4 ÷ 10 = 0.4, so 3.2 cm by 2.4 cm, area 7.68 sq cm. Check: 48 × 0.4² = 48 × 0.16 = 7.68.
5 cm below the apex: scale 0.5, so 4 cm by 3 cm, area 12 sq cm.
7.68 square centimeters; 12 square centimeters