Face — Grade 7 Accelerated, what it means and where it is taught

A flat surface; a line where two faces meet; a corner point.

Taught in Grade 7 Accelerated.

Where it is taught

What uses it later

This idea is needed for:

Practise this idea

15 questions in the course bank use Face, in Plane Sections of 3-D Figures, Surface Area & Nets. The first 8 are below; the rest are in those units.

Problem 1

A cube is sliced parallel to one of its faces. What shape is the cross section?

  1. A square
  2. A triangle
  3. A circle
  4. A hexagon
Worked answer

A square

You get a square identical to the face, no matter how deep you cut.

Problem 2

How many faces does a cube have?

Worked answer

6

6 faces.

Problem 3

What is the greatest number of sides a cross section of a cube can have?

Worked answer

6

A cube has 6 faces

A plane can be tilted to pass through all six at once

That gives a hexagon — 6 sides.

Problem 4

A cube net is a row of four squares A, B, C, D, with E above B and F below B. Which face ends up opposite A?

  1. B
  2. C
  3. D
  4. E
Worked answer

C

Folding a row of four wraps it into a band

A and C are two apart, so they face each other

Likewise B opposite D, and E opposite F.

Problem 5

A single flat cut slices off one corner of a cube. What shape is the new face?

  1. A square
  2. A triangle
  3. A pentagon
  4. A hexagon
Worked answer

A triangle

Three faces meet at a corner, so the plane crosses three faces

Three faces cut gives a triangle.

Problem 6

A cube is sliced through the diagonal of its top face and the parallel diagonal of its bottom face. What shape is the cross section?

  1. A square
  2. A rectangle
  3. A triangle
  4. A hexagon
Worked answer

A rectangle

The plane crosses four faces, so the cross section has four sides

All four corners are right angles, but the horizontal sides are diagonals — longer than the vertical edges

So it is a rectangle, not a square.

Problem 7

A cube is sliced through the three vertices next to one corner. What kind of triangle appears?

  1. A right triangle
  2. An equilateral triangle
  3. A scalene triangle
Worked answer

An equilateral triangle

Each of the three sides is a diagonal of a square face

All the faces are identical, so all three diagonals are equal

The cross section is an equilateral triangle.

Problem 8

A 5 × 4 × 3 rectangular prism is sliced parallel to its 5 × 4 face. Find the area of the cross section.

Worked answer

20

The cross section is a 5 × 4 rectangle

Area = 20, the same at every depth.

Elsewhere

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