Year 8 in England
7th grade geometry
16 7th grade geometry skills, each with a worked example, free practice that checks every answer, and a printable worksheet. Start with a mixed review, or jump to the skill you need.
Mixed review
Ten questions drawn from every skill below.
Circumference of a circle
CCSS 7.G.B.4England: KS3 GeometryEngland: GCSE Foundation Geometry
Example
A circle has radius 6 ft. Give its circumference in terms of π: it is kπ ft. What is k?
- C = 2 × π × 6 = 12π ft
Answer: 12
Builds on: Perimeter, Multiply decimals
Leads to: Area of a circle, Link radius, diameter and circumference
Area of a circle
CCSS 7.G.B.4England: KS3 GeometryEngland: GCSE Foundation Geometry
Example
A circle has diameter 14 cm. Its area is kπ cm². What is k?
- r = 14 ÷ 2 = 7
- A = π × 7² = 49π cm²
Answer: 49
Vertical, complementary and supplementary angles
CCSS 7.G.B.5England: KS3 GeometryEngland: GCSE Foundation Geometry
Example
Two straight lines cross. One angle is 23°. What is the vertically opposite angle?
- 23°
Answer: 23
Volume of prisms
CCSS 7.G.B.6England: KS3 GeometryEngland: GCSE Foundation Geometry
Example
A triangular prism has a triangular end with base 10 ft and height 12 ft. The prism is 4 ft long. What is its volume, in ft³?
- ½ × 10 × 12 = 60
- 60 × 4 = 240 ft³
Answer: 240
Scale factors and enlargement
CCSS 7.G.A.1England: KS3 GeometryEngland: GCSE Foundation Geometry
Example
A 14 cm by 4 cm rectangle is enlarged by scale factor 0.5. What is the new length in cm?
- 14 × 0.5 = 7 cm
Answer: 7
Builds on: Scale drawings and maps
Leads to: Similar shapes, Dilations (enlargements) from the origin
Link radius, diameter and circumference
CCSS 7.G.B.4England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Example
A circle has circumference 12π cm. What is its diameter, in cm?
- πd = 12π → d = 12
Answer: 12
Area and perimeter of semicircles and quarter circles
CCSS 7.G.B.4England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Example
A semicircle has diameter 8 cm. Find its perimeter (curved part + straight edge), to 1 decimal place.
- π × 8 ÷ 2 = 12.566
- + 8 = 20.566
- ≈ 20.6 cm
Answer: 20.6
Solve real problems with circles
CCSS 7.G.B.4England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Example
A bike wheel has diameter 50 cm. How far does the bike travel, in metres, when the wheel turns 91 times? Round to 1 decimal place.
- π × 50 = 157.08 cm
- × 91 = 14294.2 cm
- ≈ 142.9 m
Answer: 142.9
Use vertically opposite angles
CCSS 7.G.B.5England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Example
Two straight lines cross. One of the angles is 62°. What is the angle vertically opposite it?
- Opposite angles are equal: 62°
Answer: 62
Find complementary and supplementary angles
CCSS 7.G.B.5England: KS3 Geometry and measures
Example
What is the complement of a 14° angle?
- 90° − 14° = 76°
Answer: 76
Angles on a straight line and around a point
CCSS 7.G.B.5England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Example
Three angles sit on a straight line. Two of them are 64° and 48°. Find the third.
- 180° − 64° − 48° = 68°
Answer: 68
Builds on: Find complementary and supplementary angles
Missing angles in triangles, including isosceles and algebra
CCSS 7.G.A.2CCSS 8.G.A.5England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Example
The angles of a triangle are x, 3x and 5x. What is the largest angle, in degrees?
- 9x = 180
- x = 20
- 5 × 20 = 100°
Answer: 100
Decide whether three lengths can make a triangle
CCSS 7.G.A.2England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Example
Can sticks of length 9 cm, 2 cm and 11 cm make a triangle?
- 2 + 9 = 11 ≤ 11
- No.
Answer: No
Builds on: Classify triangles; angles in a triangle
Volume of triangular and other prisms
CCSS 7.G.B.6England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Example
A prism has a cross-section shaped like a pentagon with area 22 cm². It is 7 cm long. What is its volume, in cm³?
- 22 × 7 = 154 cm³
Answer: 154
Builds on: Volume of prisms, Area of triangles
Surface area of triangular prisms
CCSS 7.G.B.6England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Builds on: Surface area using nets, Area of triangles
Describe cross-sections of solids
CCSS 7.G.A.3England: KS3 Geometry and measures
Example
A cube is sliced parallel to one face. What shape is the cut face (cross-section)?
- The cross-section is a square.
Answer: Square
Builds on: Faces, edges and vertices of 3D shapes
Keep exploring
7th grade topic pages
More for 7th grade
Hands-on math tools
- Virtual fraction bars and fraction circles
- Interactive number line
- Virtual base ten blocks
- Multiplication arrays
- Interactive teaching clock
- Virtual money for counting practice
- Interactive coordinate plane
- Algebra balance scale
- Adding fractions with a model
- Virtual algebra tiles
- Alphabetical order game
- Virtual protractor and angle maker
- Area and perimeter builder
- Bar graph maker for kids
- Math by topicFractions, times tables, long division and more
- English and grammarNouns, verbs, commas, spelling and more
- Reading passagesShort stories with read-aloud and questions
- Science by gradePlants, forces, matter, space and more
- Printable worksheetsPrint, or do them on a tablet with a finger or pen
- Free math games3D games where every move is a math question
- Manipulatives and simulationsMath tools plus science sims: cells, atoms, forces, planets
- Fraction calculatorEvery step shown, from mixed numbers to simplest form
- Math 5-a-dayFive fresh warm-up questions every day
- Guides for parentsHow to help with fractions, tables, tests and more
Math, English and science that click.