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Triangles and quadrilaterals

Properties of 2D shapes, angle sums in triangles and quadrilaterals, and symmetry.

  • Define and explain Triangles and quadrilaterals in your own words
  • Use key terms such as Angle accurately
  • Apply what you have learned to new examples and questions
  • Avoid the common mistakes learners make with this topic

This lesson focuses on Triangles and quadrilaterals: properties of 2D shapes, angle sums in triangles and quadrilaterals, and symmetry.

Definition: Triangles and quadrilaterals

Properties of 2D shapes, angle sums in triangles and quadrilaterals, and symmetry.

Key ideas

Angle facts

Angles on a straight line add to 180 degrees, and angles around a point add to 360 degrees. In a triangle the three interior angles always sum to 180 degrees, so one missing angle can be found by subtracting the other two from 180.

Area formulae

Rectangle: base times height. Triangle: half times base times height, using the perpendicular height, not the slant side. Trapezium: half times the sum of the parallel sides times the distance between them.

Key term — Angle: The amount of turn between two lines that meet, measured in degrees. A right angle is exactly 90 degrees.

Finding a missing angle

A triangle has two angles of 52° and 73°. Find the third angle.

The three angles of any triangle add to 180°. Subtract the two known angles from 180°: 180 − 52 − 73. 180 − 52 = 128, and 128 − 73 = 55.

Answer: The third angle is 55°. Check: 52 + 73 + 55 = 180 ✓.

Common mistakes
  • Using the slant height of a triangle as its height The height must be perpendicular to the base; measure straight down to the base line, not along the slanted edge.
  • Confusing radius and diameter in circle formulae A = πr² uses the radius; C = πd uses the diameter. If given the diameter, halve it first for area.

Practice

A triangle has base 10 cm and perpendicular height 6 cm. Find its area.
Area = ½ × base × height.

Area = ½ × 10 × 6 = 30 cm².

Two angles on a straight line are 112° and x. Find x.
Angles on a straight line sum to 180°.

x = 180 − 112 = 68°.

Find the perimeter and area of a rectangle 7 cm by 4 cm.
Perimeter adds all sides; area = length × width.

Perimeter = 2(7 + 4) = 22 cm; area = 7 × 4 = 28 cm².

Find the circumference of a circle with diameter 14 cm (use π = 3.14).
C = πd.

C = 3.14 × 14 = 43.96 cm.

Quick check

Triangles and quadrilaterals — quick check

Which of these best defines "Angle"?

The amount of turn between two lines that meet, measured in degrees. A right angle is exactly 90 degrees.

A trapezium has parallel sides 8 cm and 5 cm, with height 4 cm. Find its area.

Area = ½ × (8 + 5) × 4 = ½ × 13 × 4 = 26 cm².

A circle has radius 5 cm. Find its area (use π = 3.14).

A = 3.14 × 25 = 78.5 cm².
Key takeaways
  • Triangles and quadrilaterals: properties of 2D shapes, angle sums in triangles and quadrilaterals, and symmetry.
  • Angle facts: Angles on a straight line add to 180 degrees, and angles around a point add to 360 degrees.
  • Perimeter: The total distance around the edge of a 2D shape, found by adding all its side lengths.
  • Watch out for: using the slant height of a triangle as its height
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