Grade 6 Geometry Worksheets — Circles and Angle Sums
Sixth grade geometry pulls the earlier strands together. Angles are no longer classified one at a time but summed — in a triangle, in a quadrilateral, around a point. Areas are no longer single rectangles but shapes built from two of them, or with a piece cut away. And the circle arrives, with pi and two formulas that have to be kept apart. Grade 6 offers eight separate sheets: Angle Sums in Shapes, Missing Angles, Compound Shape Area, Area of Triangles, Circumference of a Circle, Area of a Circle, Coordinates and Volume of Cuboids.
Circumference of a Circle and Area of a Circle are deliberately separate pages, because keeping the two formulas apart is the whole point. Both use pi = 3.14, and radii and diameters are chosen so every answer is exact to at most two decimal places — no rounding, no approximations creeping into the answer key.
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Geometry · Grade 6
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Grade 6 · 4 pages · A4More Grade 6 geometry skills
Each one generates a different kind of question, with its own three levels and answer key.
- Area of TrianglesMultiply the base by the height and halve it to find a triangle's area.
- Compound Shape AreaRead an L-shape, a cut-out or a composite shape off the page, split it, and add or subtract the parts.
- Missing AnglesRead a drawn straight line or a full turn, and find the angle that is missing from it.
- Angle Sums in ShapesAngles in a drawn triangle total 180° and in a quadrilateral 360°.
- CoordinatesRead, move and complete points on a printed coordinate grid.
- Volume of CuboidsFind how much space a box fills, in cubic centimeters.
- Circumference of a CircleFind the distance around a circle using π = 3.14.
- Area of a CircleFind the space inside a circle using π × radius × radius.
What each level generates
Grade 6 area of triangles — the exact skill behind each difficulty setting, straight from the generator.
- Level 1Base and height
- Level 2Extra measurements given
- Level 3Work backwards from the area
Grade levels follow the progression common to most English-language curricula — not one specific national curriculum. Every level shows exactly what it generates, so you can check the fit with your own program. See the full scope & sequence →
Splitting a compound shape
A shape made from two rectangles can be handled in two ways: add the two areas, or take the whole rectangle and subtract the piece that is missing. Compound Shape Area gives each its own level — Two rectangles joined adds, A piece cut out subtracts, and A rectangle and a triangle swaps a triangle in for one of the rectangles. Students who only ever practise the adding level will stall the first time they meet a cut-out, so work through all three. Ask for the method to be written before the arithmetic — "add" or "subtract", and which rectangles — and the marking becomes diagnostic rather than binary.
Compound shape questions are now DRAWN, which is a change from earlier versions of this page. The shape is printed to scale with a measurement written against each side, and the sentence no longer says what it is made of — an L-shaped floor is simply drawn as an L. That matters, because the old wording named the two rectangles before a student had found them, which is the one thing the sheet is for. The cut-out level shows the piece removed as its own outline inside the shape, and the triangle level marks the height of the roof with a dashed line, because that measurement is not the length of any side.
So the work now starts where it should: look at the drawing, decide where to cut it, and only then work out the sides of the pieces. Two of the numbers a student needs are usually not printed anywhere — they are differences between the ones that are. Ask for the method to be written before the arithmetic, "add" or "subtract" and which two pieces, and the marking becomes diagnostic rather than binary.
Keeping the two circle formulas apart
Circumference is 2πr and area is πr², and the reliable way to keep them straight is by units, not by memory. Circumference is a length, so it is measured in cm and uses the radius once; area is a covering, so it is measured in cm² and needs the radius twice. If an answer to an area question comes out in plain cm, the wrong formula has been used.
Watch for the diameter trap. Both cards draw the circle and mark ONE measurement on it — a line from the centre for a radius, a line right across for a diameter — so the first thing to read is which of the two is on the page. Circumference of a Circle has a From the diameter level, where the circumference is simply π × diameter, on diameters of 100 to 250 cm, so the multiplying is the longer part; Area of a Circle still needs the radius, so a drawn diameter has to be halved first. The circles are drawn the same size whatever number they carry, because a 30 cm circle cannot be printed beside its own question at the scale the other shapes use. Working with π = 3.14 throughout keeps the arithmetic honest and lets students check the size of an answer by rounding pi to 3 in their head.
One note on timing. In England circles are statutory from Key Stage 3, which opens in Year 7 — the same school year as US Grade 6 — so these two sheets sit exactly at the floor of the range England allows, while Common Core puts the same content one year later at 7.G.B.4. They are on the Grade 6 page because a student who has already met compound area and angle sums has every tool the two formulas need; a family working strictly to Common Core loses nothing by saving Circumference of a Circle and Area of a Circle until next year.
Frequently asked questions
▸What geometry is taught in Grade 6?
Typically angle sums in triangles and quadrilaterals, the area of compound shapes made from rectangles, and the circumference and area of a circle. Angle Sums in Shapes, Compound Shape Area, Circumference of a Circle and Area of a Circle each have a sheet of their own, all using pi = 3.14.
▸How do you find the circumference and area of a circle?
Circumference is 2 × π × radius, or π × diameter. Area is π × radius × radius. With π = 3.14, a circle of radius 5 cm has a circumference of 31.4 cm and an area of 78.5 cm². Circumference of a Circle and Area of a Circle are separate sheets, and both use measurements that keep every answer exact.
▸Do the angles in a quadrilateral add up to 360 degrees?
Yes. A triangle's angles total 180°, a quadrilateral's total 360°, and angles meeting at a point also total 360°. Angle Sums in Shapes covers the first two — the third angle in a triangle, then the fourth in a quadrilateral, then isosceles and right-angled cases. The around-a-point fact lives on the Missing Angles sheet.
▸How do you find the area of a compound shape?
Split it into rectangles, find each area, then add — or, if a piece has been cut out, find the whole rectangle's area and subtract the missing piece. Compound Shape Area gives each case its own level and prints the shape to scale, with the measurements it needs on its sides, so a student decides where to cut it.