Trapezoid — Geometry, what it means and where it is taught

A quadrilateral with exactly one pair of parallel sides.

Taught in Geometry.

Where it is taught

What it rests on

Work through these first if this one does not settle.

Practise this idea

13 questions in the course bank use Trapezoid, in Length and Area in 2-D Figures, Plane Sections of 3-D Figures, Volume & Surface Area of 3-D Figures, Measurement, Quadrilaterals & Polygon Properties, Area of Triangles & Quadrilaterals. The first 8 are below; the rest are in those units.

Problem 1

A trapezoid has parallel sides 7 m and 13 m, and height 6 m. Find its area.

Worked answer

60

7 + 132 = 10

10 × 6 = 60 m2

Problem 2

A square pyramid is sliced parallel to its base. What shape is the cross section?

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

A square

A square — smaller the higher up you cut.

Problem 3

A square pyramid is sliced vertically through its apex. What shape appears?

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

A triangle

A triangle, with the apex at the top of the cut.

Problem 4

A cone is sliced parallel to its base. What shape is the cross section?

  1. A triangle
  2. A circle
  3. A trapezoid
  4. An oval
Worked answer

A circle

A circle — smaller the closer you cut to the tip.

Problem 5

A prism's base is a trapezoid with parallel sides 5 and 9 and height 4. The prism is 10 long. Find its volume.

Worked answer

280

B = 5 + 92 × 4 = 28

V = 28 × 10 = 280

Problem 6

A trapezoid has parallel sides 6 and 10 and height 5. Find its area.

Worked answer

40

6 + 102 = 8

8 × 5 = 40

Problem 7

Congruent diagonals that bisect each other mean the shape is a

  1. rectangle
  2. rhombus
  3. trapezoid
  4. kite
Worked answer

rectangle

Bisecting diagonals make it a parallelogram.

Congruent diagonals upgrade it to a rectangle.

Problem 8

Perpendicular diagonals that bisect each other mean the shape is a

  1. rhombus
  2. rectangle
  3. trapezoid
  4. square
Worked answer

rhombus

Bisecting makes it a parallelogram.

Perpendicular makes it a rhombus.

Elsewhere

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