Reference · module 7
Geometry
Everything this module explains, on one page.
Angles
Find missing angles on a line, around a point and in a triangle.
- An angle measures a turn, in degrees. A full turn is 360°, a half turn is 180°, and a quarter turn — a right angle, like the corner of a page — is 90°.
- Angles on a straight line add up to 180°. If one of them is 130°, the other is 50°. Angles all the way round a point add up to 360°.
- The three angles of any triangle add up to 180°, however it is drawn. Know two of them and the third is 180° minus their sum.
The mistake you are about to make
angles of a triangle = 360°
angles of a triangle = 180°
A full turn is 360°, and walking round a triangle feels like a full turn. Its three inside angles only make a straight line: 180°.
Perimeter and area
Tell perimeter from area and work out both for rectangles and triangles.
- Perimeter is the distance around a shape: add up all its sides. A rectangle 5 m by 3 m has a perimeter of 5 + 3 + 5 + 3, which is 16 m.
- Area is how much surface a shape covers, in square units. A rectangle's area is length times width: 5 m by 3 m covers 15 square metres, written 15 m².
- A triangle is half of a rectangle with the same base and height, so its area is base × height ÷ 2. The height is measured straight up from the base, not along a slanted side.
The mistake you are about to make
5 m × 3 m = 16 m²
5 m × 3 m = 15 m²
Perimeter and area use the same two numbers, so the formulas blur. Perimeter adds the sides and is in metres; area multiplies them and is in square metres.
Circles
Use radius, diameter and π to find the length and area of a circle.
- The radius runs from the centre of a circle to its edge; the diameter runs right across through the centre and is twice the radius. A radius of 4 cm means a diameter of 8 cm.
- The distance around a circle, its circumference, is π times the diameter. π is about 3.14, so a wheel 50 cm across rolls about 157 cm in one turn.
- The area of a circle is π times the radius squared: πr². For a radius of 10 m that is about 3.14 × 100, which is 314 m². Square the radius first, then multiply.
The mistake you are about to make
r = 10 → area = 3.14 × 20
r = 10 → area = 3.14 × 100
The 2 in r² looks like times two, which is how the diameter works. Squared means the radius times itself: 10 × 10, not 10 × 2.