Compare parallel slices through right prisms and pyramids.
Example 1
Two slices are made at different positions inside a right rectangular prism. Both slicing planes are parallel to its rectangular bases. The first cross-section is 18cm by 7cm. What is the area of the second cross-section, in square centimetres?
Show worked answer
Answer: 126
Parallel sections through this prism have the same rectangular shape and size. The second section is also 18cm by 7cm.
Area =18×7=126 square centimetres.
Example 2
The two solids are a right square prism and a square pyramid. Each is cut parallel to its base at one-third and two-thirds of its height above the base. The table shows the side lengths of the square cross-sections. Which solid is the prism?
Parallel square cross-sections
Height above base
Solid A: side (cm)
Solid B: side (cm)
One-third of height
12
20
Two-thirds of height
6
20
Show worked answer
Answer: Solid B
The prism has parallel cross-sections of the same shape and size: square sides of 20cm at both heights.
The pyramid's square sides decrease from 12cm to 6cm toward its apex. The prism is therefore Solid B.
Example 3
A right prism has regular triangle-shaped bases. Each base has 3 equal sides of 3cm. A slice is made parallel to the bases, strictly inside the prism. Which shape and perimeter describe the cross-section?
Right prismDiagram not to scaleShow worked answer
Answer: triangle; perimeter 9cm
A parallel section has the same shape and size as a base: a triangle with 3 sides of 3cm.
Its perimeter is 3×3=9cm.
Right prisms and parallel cross-sections practice | Year 6 | Ascent Arcade