Year 6: Drawing 2-D shapes from their dimensions and angles
Part of the Year 6 angles, shapes and circles chapter. Chapter overview · whole chapter on one page
Drawing 2-D shapes from their dimensions and angles
When you draw a shape, the question gives you its dimensions: some lengths and some angles. Use a ruler for the lengths and a protractor for the angles. Mark each corner with a letter, so you can name the shape.
Once a shape is drawn, you can still use the angle rules. A triangle still has angles that add up to 180°, and a quadrilateral has angles that add up to 360°. You can also add up the sides to find the perimeter, and check that the sides can make a shape at all.
A drawing must be accurate, which means it is drawn to the lengths and angles that are given. A picture that is not to scale does not use the true sizes, so do not measure it.
Key ideas
- Use a ruler for the lengths and a protractor for the angles.
- Name each corner with a capital letter.
- A triangle drawn with two angles has the third angle left over: 180 minus the two.
- The perimeter is the sum of all the sides.
Key words. The interior angles are the angles inside a shape. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Add the angles you know, then take them away from the total for a triangle.
- Remember the total for a triangle. The three angles in any triangle add up to 180 degrees.Total = 180°
- Add the angles you know. Put them together to see how much of the total is used.40° + 75° = 115°
- Take the angles you know away from the total. What is left over is the missing angle.180 - 115 = 65
- Write the answer. The missing angle is 65 degrees.65
Check. 65 + 115 = 180, so the angles add up correctly. ✓
Watch out. A triangle has 180 degrees in total, not 360. Quadrilaterals have 360.
Key words. The interior angles are the angles inside a shape. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal.
Method. Find the length of each of the four sides, then add them up.
- Write down the lengths of the sides. A parallelogram has two sides of each length: the base, and the slanted side.base = 8 cm, slanted side = 5 cm
- Add the four sides. The sides are 8, 5, 8 and 5. The angles do not change the perimeter.8 + 5 + 8 + 5 = 26
- Write the answer. The perimeter is in centimetres.26
Check. 2 × (8 + 5) = 26, the same answer. ✓
Watch out. The angles are not needed for the perimeter. Use only the lengths of the sides.
Key words. The interior angles are the angles inside a shape. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal.
Method. Take the top angle from 180, then share what is left equally between the two base angles.
- Remember: the three angles of a triangle add up to 180 degrees. So the top angle and the two base angles share 180.180 total
- Take the top angle away. This leaves the two base angles together.180 - 120 = 60
- Share the rest equally between the two base angles. The two base angles are equal, so divide by 2.60 ÷ 2 = 30
- Write the answer. Each base angle is this size.30
Check. 30 + 30 + 120 = 180. ✓
Watch out. Only divide the rest by 2. Do not divide the top angle.
Exercise 10E Practice: drawing and checking shapes
Non-calculatorKey words. The interior angles are the angles inside a shape. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal.
Method. Add the lengths of all the sides.
- Add the lengths of all the sides. The perimeter is the distance all the way round the outside.6 + 4 + 6 + 4 = 20
- Write the answer. The perimeter is in cm.20
Check. Go round the shape once more and check that each side is counted once. ✓
Watch out. Count every side once. Do not forget the sides you cannot see on a drawing.
Key words. The interior angles are the angles inside a shape. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal.
Method. Add the lengths of all the sides.
- Add the lengths of all the sides. The perimeter is the distance all the way round the outside.4.5 + 4.5 + 4.5 + 4.5 = 18
- Write the answer. The perimeter is in cm.18
Check. Go round the shape once more and check that each side is counted once. ✓
Watch out. Count every side once. Do not forget the sides you cannot see on a drawing.
Key words. The interior angles are the angles inside a shape. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal.
Method. Add the lengths of all the sides.
- Add the lengths of all the sides. The perimeter is the distance all the way round the outside.6 + 6 + 4 = 16
- Write the answer. The perimeter is in cm.16
Check. Go round the shape once more and check that each side is counted once. ✓
Watch out. Count every side once. Do not forget the sides you cannot see on a drawing.
Key words. The interior angles are the angles inside a shape. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Add the angles you know, then take them away from the total for a triangle.
- Remember the total for a triangle. The three angles in any triangle add up to 180 degrees.Total = 180°
- Add the angles you know. Put them together to see how much of the total is used.52° + 48° = 100°
- Take the angles you know away from the total. What is left over is the missing angle.180 - 100 = 80
- Write the answer. The missing angle is 80 degrees.80
Check. 80 + 100 = 180, so the angles add up correctly. ✓
Watch out. A triangle has 180 degrees in total, not 360. Quadrilaterals have 360.
Key words. The interior angles are the angles inside a shape. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal.
Method. Take the top angle from 180, then share what is left equally between the two base angles.
- Remember: the three angles of a triangle add up to 180 degrees. So the top angle and the two base angles share 180.180 total
- Take the top angle away. This leaves the two base angles together.180 - 40 = 140
- Share the rest equally between the two base angles. The two base angles are equal, so divide by 2.140 ÷ 2 = 70
- Write the answer. Each base angle is this size.70
Check. 70 + 70 + 40 = 180. ✓
Watch out. Only divide the rest by 2. Do not divide the top angle.
Key words. The interior angles are the angles inside a shape. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Add the angles you know, then take them away from the total for a quadrilateral.
- Remember the total for a quadrilateral. The four angles in any quadrilateral add up to 360 degrees. A diagonal splits it into two triangles, and 2 × 180 = 360.Total = 360°
- Add the angles you know. Put them together to see how much of the total is used.90° + 90° + 60° = 240°
- Take the angles you know away from the total. What is left over is the missing angle.360 - 240 = 120
- Write the answer. The missing angle is 120 degrees.120
Check. 120 + 240 = 360, so the angles add up correctly. ✓
Watch out. A four-sided shape has 360 degrees in total. Do not use 180.
Key words. The interior angles are the angles inside a shape. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal.
Method. Add the lengths of all the sides.
- Add the lengths of all the sides. The perimeter is the distance all the way round the outside.4 + 4 + 4 + 4 + 4 = 20
- Write the answer. The perimeter is in cm.20
Check. Go round the shape once more and check that each side is counted once. ✓
Watch out. Count every side once. Do not forget the sides you cannot see on a drawing.
Key words. The interior angles are the angles inside a shape. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal.
Method. Add the lengths of all the sides.
- Add the lengths of all the sides. The perimeter is the distance all the way round the outside.5.5 + 5.5 + 5.5 + 5.5 = 22
- Write the answer. The perimeter is in cm.22
Check. Go round the shape once more and check that each side is counted once. ✓
Watch out. Count every side once. Do not forget the sides you cannot see on a drawing.
Key words. The interior angles are the angles inside a shape. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Add the angles you know, then take them away from the total for a triangle.
- Remember the total for a triangle. The three angles in any triangle add up to 180 degrees.Total = 180°
- Add the angles you know. Put them together to see how much of the total is used.35° + 90° = 125°
- Take the angles you know away from the total. What is left over is the missing angle.180 - 125 = 55
- Write the answer. The missing angle is 55 degrees.55
Check. 55 + 125 = 180, so the angles add up correctly. ✓
Watch out. A triangle has 180 degrees in total, not 360. Quadrilaterals have 360.
Key words. The interior angles are the angles inside a shape. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal.
Method. Add the lengths of all the sides.
- Add the lengths of all the sides. The perimeter is the distance all the way round the outside.7 + 7 + 2 + 2 = 18
- Write the answer. The perimeter is in cm.18
Check. Go round the shape once more and check that each side is counted once. ✓
Watch out. Count every side once. Do not forget the sides you cannot see on a drawing.
Key words. To draw a shape from its dimensions, use a ruler for the lengths and a protractor for the angles. A dimension is a length or an angle that gives the size of a shape.
Method. Check whether the two shorter sides can reach across to the longest side.
- Add the two shorter sides. The two shorter sides must be able to reach the longest side.3 + 4 = 7
- Compare with the longest side. The longest side is 8 cm, which is longer than 7 cm.7 is less than 8
- Write the answer. The sides cannot meet, so the triangle cannot be drawn.No
Check. A triangle with sides 3 cm, 4 cm and 5 cm can be drawn, because 3 + 4 is more than 5. ✓
Watch out. Two short sides must add up to more than the longest side.
Key words. To draw a shape from its dimensions, use a ruler for the lengths and a protractor for the angles. A dimension is a length or an angle that gives the size of a shape.
Method. Split the rectangle into two triangles with the diagonal, and add the angles of each triangle.
- Find the angles in one triangle. Each triangle has angles that add up to 180 degrees.180 degrees
- Find the angles in the other triangle. The second triangle also has angles that add up to 180 degrees.180 degrees
- Add the two totals. This gives all the angles in both triangles.180 + 180 = 360
- Write the answer. The total of all the angles in both triangles is 360 degrees.360
Check. This is the same as the four angles of a quadrilateral, which also add up to 360. ✓
Watch out. The total of two triangles is 360, not 180. Each triangle gives 180.
Watch out
Common mistake: measuring a diagram that is not drawn to scale. Use the numbers that the question gives. Also, when a triangle is drawn with two angles, the third is 180 minus the other two, not 360.
Exam tip
Before you draw, check the dimensions. Two short sides must be long enough to reach the longest side.