area problem solving ks3

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Key Stage 3 - Geometry

Standard KS3.G.1.1 - Calculate the area and perimeter of rectangles and squares with word problems.

Included Skills:

Geometry and measures • Pupils should be taught to: - derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders) - calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes - draw and measure line segments and angles in geometric figures, including interpreting scale drawings - derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line - describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric - use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles - derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies - identify properties of, and describe the results of, translations, rotations and reflections applied to given figures - identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids - apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles - understand and use the relationship between parallel lines and alternate and corresponding angles - derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons - apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras' Theorem, and use known results to obtain simple proofs - use Pythagoras' Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles - use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D - interpret mathematical relationships both algebraically and geometrically.

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Visual maths worksheets, each maths worksheet is differentiated and visual.

KS3 Area and Perimeter Worksheets

Maths Worksheets / KS3 Area and Perimeter Worksheets

Area of Non-Right Angled Triangles

Area of Quadrilaterals (A)

Area of Right Angled Triangles

Compound Shapes (A)

Tiling Problems (A)

Area and Circumference

Area of 2D shapes

Area of Circles

Area of Quadrilaterals (B)

Area of Trapezia (A)

Area of Trapezia (B)

Circle Area Problems

Circumference

Compound Shapes (B)

Solving Equations Involving Area of Rectangles

Area of Sectors and Arc Lengths

Finding the Radius or Diameter

Surface Area of Cones and Spheres

Surface Area of Prisms

The Formulae for Area of Sectors and Arc Lengths

Area of Sectors and Segments

Area of Sectors and Segments (With Clues)

Area of Triangles (With Clues)

Printable Area and Perimeter Worksheets With Answers

Why is learning about area and perimeter important.

Calculating perimeters and areas is an important skill which is used by many people in their everyday lives.

Architects, engineers and construction workers will need precise measurements of area and perimeter in order to construct a building to the right specification. It is not just professionals that need a solid knowledge of area and perimeter; knowing the area of a room can help work out how much paint or flooring is needed to fill the space when redecorating.

Improve Students’ Problem Solving Skills

Regularly practicing area and perimeter questions with children can help them develop good problem solving and logic skills.

The importance of these skills should not be underestimated, as these skills are useful for their learning in other subjects, as well as preparing them for the workplace.

Worksheets Make Learning Area and Perimeter Enjoyable

Children start learning about perimeters and areas in KS2, so it is important to use area and perimeter materials which make the topic easy to understand and enjoyable for them.

Worksheets with fun activities help children learn about this important area of maths. Using good quality resources throughout their education will prepare children for more advanced area and perimeter questions, such as calculating areas of compound shapes and areas of sectors.

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Resources you can trust

Area challenge

This area of 2D shapes activity is a general review and revision task for either for KS3 or for Foundation GCSE maths. Students need to work backwards from area to find lengths on a square, triangle, parallelogram, two trapezia and a circle.

Other than the circle, all lengths and areas are integers and answers are included.

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Perimeter, Area and Volume - Stage 3

Perimeter and Area

This selection of problems is a great starting point for learning about Perimeter and Area.

Surface Area and Volume

This selection of problems is a great starting point for learning about Surface Area and Volume

Blue and White

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

An Unusual Shape

Can you maximise the area available to a grazing goat?

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

On the Edge

If you move the tiles around, can you make squares with different coloured edges?

Sending a Parcel

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Efficient Cutting

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

Isosceles Triangles

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Can They Be Equal?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Cuboid Challenge

What's the largest volume of box you can make from a square of paper?

Changing Areas, Changing Perimeters

How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?

Changing Areas, Changing Volumes

How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

Perimeter Possibilities

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

Triangles in a Square

What are the possible areas of triangles drawn in a square?

Perimeter Challenge

Can you deduce the perimeters of the shapes from the information given?

Colourful Cube

A colourful cube is made from little red and yellow cubes. But can you work out how many of each?

Isometric Areas

We usually use squares to measure area, but what if we use triangles instead?

More Isometric Areas

Isometric Areas explored areas of parallelograms in triangular units. Here we explore areas of triangles...

Perimeter, Area and Volume Short Problems

A collection of short problems on area and volume.

Shear Magic

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

Triangle in a Trapezium

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

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Area and Perimeter

This SMILE resource contains three packs of games, investigations, worksheets and practical activities supporting the teaching and learning of area and perimeter, from calculating area by counting squares to finding the formula for the area of a trapezium.

Area and Perimeter pack one  contains fourteen work cards with a wide variety of activities covering finding areas by counting squares, finding the length of perimeters by counting, developing the formula for the area of a rectangle, drawing different shapes with a given perimeter, finding different shapes with a given area and finding the area of simple compound shapes.

Area and Perimeter pack two  contains eleven work cards with activities requiring students to make shapes of a given size using pentominoes, investigate the area and perimeter of rectangles, find the area of a right-angled triangle, calculate the area of polygons drawn on square dotted paper, investigate different ways of shading half a square, find the area of a triangle, find the area of compound shapes made from rectangles and find the area of a parallelogram.

Area and Perimeter pack three  contains eleven work cards with activities in which students investigate the connections between the area of a parallelogram and the area of a rectangle, the area of obtuse-angled triangles, further parallelogram problems, finding the area of a polygon, finding the area of a trapezium and calculating the area of irregular shapes.

SMILE (Secondary Mathematics Individualised Learning Experiment) was initially developed as a series of practical activities for secondary school students by practising teachers in the 1970s. It became a complete individualised scheme based around a network of activity cards and assessments. Related resources include answers  to all of the cards and test books and answers .

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Area of Compound Shapes Practice Questions

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• Problem Solving Question Of The Day Compilation Worksheets For Ks3 Maths

KS3 maths worksheets – 100+ problem-solving questions

PDF question and answer booklets

This KS3 maths worksheets booklet from White Rose Maths contains over 100 problem-solving questions. There’s also an answer booklet.

You can also use these questions with GCSE pupils. Some problems are suitable for foundation and higher. Others are suitable for higher tier only.

Example KS3 maths worksheets questions

Max is saving to buy a computer game that costs £26. He saves 5p, 10p and 50p coins in a jar. The ratio of 5p to 10p to 50p coins is 2 : 5 : 1. There are 120 coins in the jar. How much more does he need to save?

You want to cover the floor in carpet titles. The tiles measure 40cm by 40cm. The floor is 3.2m by 2m. Tiles are sold in boxes of 12. How many boxes of tiles will you need to cover the floor?

Richard is doing a survey. He asks people to choose their favourite biscuits. THere are four biscuits: A, B, C or D. Here are the results: A (?); B (20%), C (15%), D (30%). 160 people chose B. How many people chose A?

White Rose Maths provides high-quality, research-driven KS3 and GCSE maths resources to support teaching and learning. Follow on Twitter at  @whiteroseed . Browse more maths worksheet packs for Years  7 ,  8  and  9 and a list of  GCSE maths games .

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KS2/KS3 Area/Perimeter Problems - Year 5, 6, 7, 8

Subject: Mathematics

Age range: 7-11

Resource type: Other

Last updated

25 February 2021

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Having looked online at various area and perimeter questions, i felt they were all too similar, with very little problem solving/investigation skills being used. So, I decided to create these. They are different from other activities i found, and i feel fit brilliantly with the new curriculum.

I created these resources myself, and have used them in a class where i have got children from every year in ks2. They love problem solving and it was a hit in my class.

Please leave a comment and share your views. This will only aid in future production of resources.

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PrimaryEducator1989

A nice alternative to White Rose and similar resources! We used the problems as a discussion point in class and children really enjoyed the challenge. Thanks.

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Thanks for sharing. Very useful.

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Retired firefighter teaches problem-solving skills to Indy-area kids

INDIANAPOLIS (WISH) — A retired Indianapolis firefighter is igniting leadership in Indianapolis. He created an organization to teach problem-solving skills to as many kids as possible.

In 1992, Anthony Williamson co-founded a youth leadership and development program named after Saint Florian, the patron saint of firefighters.

The Saint Florian Center began as a summer camp and evolved into a year-round youth program. Their motto is “to foster leadership opportunity and respect in all neighborhoods.”

“They have to be able to think about what they do before they act and then they can go and respond in an appropriate way. So many times our kids get into trouble because somebody steps on their shoes or they call them out of their name and they just respond and react and we don’t want them to react,” Williamson explained to News 8’s Brittany Noble.

The center now offers a variety of  programs including youth employment training, college prep, Readers are Leaders , and Rites of Passage.

“We were contacted by (a school) principal because they had some young people, specifically boys, that seemed to not understand community, not understand how to remain focused on their classwork and not be disruptive in the classroom, therefore, they were sent to the office on multiple occasions. So they were looking for ways on how to empower young people to understand why education is so important,” Williamson said.

The  Saint Florian Center  thrives on volunteers to expand their reach. So far, Williamson says he’s worked with more than 30,000 kids but he hopes he can reach more children.

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