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Area of Parallelograms: Free Printable Worksheet for Year 6

  • ForYear 6
  • StageKey Stage 2
  • CostFree
  • FormatPrintable PDF
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Area of Parallelograms is a free printable maths worksheet for Year 6 (ages 10 to 11). Children use base times height to find the area of parallelograms, with lengths in centimetres. One question works backwards from a known area. It takes about 15 minutes, needs only a pencil, and page 2 gives the grown up notes, help ideas, a stretch task and the answers.

It comes from the Mini Minds Hub, the free library of printables from Jaques of London, the British games and toy company that has been making games for families since 1795. Print both pages, give page 1 to your child and keep page 2 for yourself. Black and white printing works well.

What is on the sheet

Children are given the base and the height of a parallelogram, all in centimetres, and work out the area. The numbers change from question to question, so they practise the same method on different multiplications. One question flips the task. It gives the area and the base, and children work out the missing height. There is space to answer under each question, and a quick sketch helps.

  • Base 8 cm, height 5 cm. What is the area?
  • Base 12 cm, height 6 cm. What is the area?
  • Base 9 cm, height 4 cm. What is the area?
  • Base 15 cm, height 7 cm. What is the area?
  • Base 20 cm, height 3 cm. What is the area?
  • Base 11 cm, height 8 cm. What is the area?
  • Base 14 cm, height 5 cm. What is the area?
  • The area is 54 cm2 and the base is 9 cm. What is the height?

Worked example

A parallelogram has a base of 13 cm, a perpendicular height of 6 cm and a slanted side of 7 cm. What is its area?

This question is not on the sheet. It shows two ways children can think about it.

Method 1: split the multiplication
  1. Pick out the base and the perpendicular height: 13 cm and 6 cm.
  2. Split 13 into 10 and 3.
  3. 10 × 6 = 60 and 3 × 6 = 18.
  4. Add the parts: 60 + 18 = 78.
Method 2: make a rectangle
  1. Sketch the parallelogram. Imagine cutting a triangle off one slanted end and sliding it to the other end.
  2. The new shape is a rectangle that is 13 cm long and 6 cm tall.
  3. Work out 13 × 6. Do 13 × 3 = 39, then double it: 78.
78 cm²

Ways to build understanding

Start with a rectangle

Ask your child to find the area of a rectangle first. Then show a parallelogram with the same base and height. Talk about what looks the same and what looks different.

Cut and slide

Draw a parallelogram on paper and cut it out. Cut off a triangle from one end and slide it to the other end. Children see the rectangle appear.

Label before calculating

Ask children to mark the base and the perpendicular height on every sketch before they multiply. It builds a habit that stops slips.

Work backwards

Once a child can find area, give an area and a base and ask for the height. Check by multiplying the answer back.

Where parallelograms appear

A parallelogram is a four sided shape with two pairs of parallel sides. Opposite sides are the same length. You can spot the shape in tile and brick patterns, in fabric designs and in folding gates that stretch and squash. Children often meet it as a rectangle that has been pushed over to one side, which is a useful way to picture it.

Area tells us how much flat space a shape covers. We measure it in square units, such as square centimetres, written cm². Children already know that the area of a rectangle comes from multiplying two lengths. Parallelograms build on that idea. Seeing how the two shapes are linked makes the method easier to remember than a rule on its own.

Careful sketching matters here. Many children measure whatever length is nearest. Drawing the shape and labelling the lengths slows them down and helps them choose the right ones.

Skills and curriculum link

  • Finding area
  • Multiplying
  • Geometry
  • Reading a diagram
  • Working backwards

This sheet supports the area below. It is matched to the published England framework. Please check it against your own school plan.

Framework Subject or area Strand Year
National Curriculum (England) Maths Measurement Year 6

What children will be able to do

  • I can find the area of a parallelogram.
  • I can multiply the base by the perpendicular height.
  • I can tell the height from the slanted side.

Handy ideas for parallelograms

  • Parallel sidesA parallelogram has two pairs of parallel sides. Opposite sides are equal in length.
  • Square unitsArea is counted in squares. Centimetre measurements give an answer in square centimetres, cm².
  • Rectangles are specialA rectangle is a parallelogram with square corners. Its area method links to the parallelogram method.
  • Undoing multiplicationMultiplication and division undo each other. This helps when one measurement is missing and the area is known.

Key words

  • ParallelogramA four sided shape with two pairs of parallel sides.
  • BaseThe side the shape sits on. We measure the height from it.
  • Perpendicular heightThe distance between the base and the opposite side, measured at a right angle to the base.
  • AreaThe amount of flat space inside a shape.
  • Square centimetreA unit for area. It is the size of a square with sides of 1 cm. We write it cm².
  • Slanted sideA leaning edge of a parallelogram. It is not the same as the height.

How to use it

  1. Print both pages. Page 1 is for your child. Keep page 2, which has the notes and answers.
  2. Read the first question together. Ask your child to sketch the parallelogram and label the base and the height.
  3. Let them multiply in their own way. Partitioning, a written method or doubling and halving are all fine.
  4. Check with page 2. Ask, "How did you work that out?" The reasoning matters as much as the answer.
  5. Come back another day and redo any tricky questions. Repeating a familiar sheet builds confidence.

Help, stretch and game ideas

If it feels too hard

Draw the shape on squared paper and count the squares. Move the triangle from one end to the other to make a rectangle. Then multiply the two sides of the rectangle. Try the first few questions first and come back to the rest later.

To stretch confident children

Make up your own base and height and ask a friend to find the area. Then try one the other way round. Give an area and a base and ask your friend to find the height. Check each answer by multiplying.

Make it a game

Roll two dice, one for the base and one for the height. Draw the parallelogram quickly and race a friend to work out the area. The fastest correct answer scores a point. First to five points wins.

Mistakes to watch for

Watch forA child multiplies the base by the slanted side instead of the height.

Try thisAsk them to find the line that makes a right angle with the base. Draw it in with a ruler and label it before multiplying.

Watch forA child adds the base and height instead of multiplying.

Try thisGo back to a rectangle on squared paper. Count the squares in rows and show that area comes from rows times columns.

Watch forA child writes the answer in cm instead of cm².

Try thisExplain that area counts squares, not lengths. Practise saying "square centimetres" and writing the small 2 every time.

Talk about it

  • How do you know which length is the height?
  • What does the area of a parallelogram tell you?
  • How could you turn a parallelogram into a rectangle?
  • Why do we write cm² and not cm?
  • How could you check your answer is sensible?
  • If you know the area and the base, how could you find the height?

Take it off the page

Paper parallelograms

Draw parallelograms on squared paper. Cut them out, then cut off a triangle and slide it across. Stick down the rectangle and write its area.

Shape hunt

Look around the house or classroom for parallelograms in patterns, tiles or packaging. Sketch them and label a base and a height.

Design a pattern

Make a pattern from parallelograms of different sizes. Work out the area of three of them and write the numbers inside.

Who it is for

Parents

Sit beside your child for the first question, then let them lead. Ten to fifteen minutes is plenty. If they get stuck, ask them to sketch the shape and label the base and height.

Teachers

Use it as a starter, a plenary after teaching area, an early finisher task or homework. Page 2 gives support and stretch for mixed ability groups. It needs only printing.

Home educators

Pair it with squared paper, scissors and a ruler. Short bursts work well. You can print it again for brothers and sisters, or for revision a few weeks later.

Where this fits in maths

Before this, children learn to find the area of rectangles by multiplying and by counting squares. They also learn what perpendicular and parallel mean. Fluent multiplication helps a lot, so practise times tables alongside this sheet.

After this, children move on to the area of triangles, which links closely to parallelograms. They also meet area in compound shapes, and later volume. All of these use the same habit: choose the right measurements, then calculate carefully.

Check it worked

Ask these when the sheet is finished. Listen for the reasoning, not just the answer.

  1. Which measurement do you use for the height?
  2. Why is the slanted side not used in the area?
  3. How could you turn a parallelogram into a rectangle?

Questions parents and teachers ask

What age is Area of Parallelograms for?

It is written for Year 6 (ages 10 to 11), in Key Stage 2. Children need to be confident multiplying two digit numbers by one digit numbers, and to know what area means.

What will children practise?

They find the area of a parallelogram by multiplying the base by the perpendicular height. They also practise reading measurements from a sketch and working backwards to find a missing height.

What if my child mixes up the height and the slanted side?

Draw the shape and ask them to mark the line that makes a right angle with the base. Label it before multiplying. Doing this on every question soon makes it a habit.

Do children need a calculator?

No. The numbers are chosen so children can multiply on paper or in their heads. Partitioning, such as splitting a number into tens and ones, is a good method to use.

Is the sheet free?

Yes. It is free to print for home and classroom use. Print it on plain A4 paper, in black and white if you prefer.

Can I use it in class?

Yes. Teachers can use it as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing, and page 2 offers support and stretch ideas.

How long does it take?

Most children finish page 1 in 10 to 20 minutes. Short sessions work best. Children who need more time can do a few questions at a time and return to the rest on another day.

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Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.

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