perimeter area and volume problem solving worksheets

Perimeter Area and Volume Worksheets

The perimeter area and volume worksheets are beneficial for kids to learn the important geometrical shapes, their properties, concepts, and their applications. Learning to calculate the perimeter, area, and volume of shapes is an important life skill and is vastly applied in real-life problem-solving. These worksheets are one of the simplest ways to teach this concept and its applications.

Benefits of the Perimeter Area and Volume Worksheets

The perimeter area and volume worksheets cover interactive exercises and problems focused on promoting understanding of the area, volume, and perimeter of various shapes and their attributes. They are an excellent way of encouraging active learning in kids for mathematical problem-solving. By solving the questions included in these worksheets, students can quickly learn the advanced geometrical concepts with ease.

Download Perimeter Area and Volume Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

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Perimeter, Area and Volume Short Problems

This is part of our collection of Short Problems . You may also be interested in our longer problems on Perimeter, Area and Volume Age 11-14 and Age 14-16 . Printable worksheets containing selections of these problems are available here:

Mid-point Area

M is the midpoint of the side of the rectangle. What is the area (in square units) of the triangle PMR?

Six Circles

In the diagram, six circles of equal size touch adjacent circles and the sides of the large rectangle. What is the perimeter of the large rectangle?

Which of the areas shown in the hexagons are equal to each other?

Nested Squares

What proportion of the diagram is shaded?

Giant Rubik's Cube

How many cubes would be visible in a 12 by 12 by 12 Rubik’s cube?

Squares in a Square

In the diagram, the small squares are all the same size. What fraction of the large square is shaded?

Cuboid Faces

Can you find the volume of a cuboid, given the areas of its faces?

Chequered Cuboid

A large cuboid is made from cubes of equal size. What fraction of the surface area of the large cuboid is black?

Star in a Hexagon

Weekly Problem 20 - 2017 The diagram shows a design formed by drawing six lines in a regular hexagon. What fraction of the hexagon is shaded?

Which of the following shaded regions has an area different from the other shaded regions?

Weekly Problem 23 - 2017 Three small equilateral triangles of the same size are cut from the corners of a larger equilateral triangle. What is the side length of the small triangles?

Exactly Three-quarters

Weekly Problem 30 - 2007 Three-quarters of the area of the rectangle has been shaded. What is the length of x?

Weekly Problem 28 - 2006 What can you say about the rectangles that form this L-shape?

Leaning Over

Weekly Problem 31 - 2017 The triangle HIJ has the same area as the square FGHI. What is the distance from J to the line extended through F and G?

Line of Squares

Weekly Problem 35 - 2016 What is the total perimeter of the squares, if the line GH in the diagram is 24cm?

Intersecting Squares

Weekly Problem 32 - 2014 Three overlapping squares are shown. If you know the areas of the overlapping and non-overlapping parts, can you work out the side lengths of the squares?

Christmas Cut-out

Weekly Problem 52 - 2017 Sue cuts some squares from a piece of paper to make a Christmas decoration. What is the perimeter of the resulting shape?

Weekly Problem 16 - 2008 A 30cm x 40cm page of a book includes a 2cm margin on each side... What percentage of the page is occupied by the margins?

Sideways Ratio

Weekly Problem 33 - 2014 A rectangle with area $125\text{cm}^2$ has sides in the ratio $4:5$. What is the perimeter of the rectangle?

Dividing a Square

A square is divided into three shapes which all have equal areas. Can you find the length of this side?

Cubic Masterpiece

Weekly Problem 49 - 2014 A blue cube is cut into 27 smaller cubes of equal size. What fraction of the total surface area of these cubes is blue?

Scalene Area

Can you find the area of this scalene triangle?

Double Cover

Weekly Problem 3 - 2007 What is the ratio of the area of the table covered twice, to the uncovered area?

Semicircle Shape

Find the shaded area of these shapes with perimeters made of semicircles.

Weekly Problem 9 - 2006 What fraction of the area of the rectangle is shaded?

Tangram Area

Weekly Problem 29 - 2008 The seven pieces in this 12 cm by 12 cm square make a Tangram set. What is the area of the shaded parallelogram?

Tile Border

What is the largest possible number of yellow tiles in this pattern?

If the area of a face of a cuboid is one quarter of the area of each of the other two visible faces, what is the area of these faces?

Open the Box

Weekly Problem 37 - 2015 A piece of card is folded to make an open box. Given its surface area, can you work out its volume?

Triangles' Triangle

Weekly Problem 27 - 2009 The perimeter of a large triangle is 24 cm. What is the total length of the black lines used to draw the figure?

Strawberries and Peas

Weekly Problem 17 - 2017 Yasmin lengthened one side of her pea bed by 3m to make it a square. This reduced her strawberry patch by $15m^2$. What was the original area of her pea bed?

Tilted Tank

Can you find the height of the water in this tilted tank when it is flat?

Cubes on a Cube

Weekly Problem 26 - 2016 A cube has each of its faces covered by one face of an identical cube, making a solid as shown. What is the surface area of the solid?

Packing Small Boxes

How many small boxes will fit inside the big box?

Hawaiian Earring

What fraction of the larger circle is outside the smaller circle?

Pile Driver

Weekly Problem 38 - 2015 Where does the line through P that halves the figure shown meet the edge XY?

Four Square

Weekly Problem 17 - 2015 A square contains two overlapping squares. What is the total of the shaded regions?

Hexagon Slices

Weekly Problem 37 - 2007 This regular hexagon has been divided into four trapezia and one hexagon.... what is the ratio of the lengths of sides p, q and r?

Triangle in a Hexagon

Weekly Problem 3 - 2009 What fraction of the area of this regular hexagon is the shaded triangle?

Rectangle Split

Draw another line through the centre of this rectangle to split it into 4 pieces of equal area.

Semicircle Stack

What is the total area enclosed by the three semicicles?

Bobbly Perimeter

Find the perimeter of this shape made of semicircles

Ratio of Areas

What is the ratio of the area of the hexagon to the area of the triangle?

Penny Farthing

Boris' bicycle has a smaller back wheel than front wheel. Can you work out how many revolutions the front wheel made if the back wheel did 120,000?

Four semicircles are drawn on a line to form a shape. What is the area of this shape?

Crazy Shading

Can you work out the fraction of the larger square that is covered by the shaded area?

Semicircular Design

Weekly Problem 9 - 2016 The diagram to the right shows a logo made from semi-circular arcs. What fraction of the logo is shaded?

The circle of radius 4cm is divided into four congruent parts by arcs of radius 2cm as shown. What is the length of the perimeter of one of the parts, in cm?

Annulus Area

Weekly Problem 38 - 2011 Given three concentric circles, shade in the annulus formed by the smaller two. What percentage of the larger circle is now shaded?

What is the area of the shape enclosed by the line and arcs?

Canny Fraction

What fraction of the volume of this can is filled with lemonade?

Loo Roll Emergency

When the roll of toilet paper is half as wide, what percentage of the paper is left?

Rectangle Cutting

Tom and Jerry start with identical sheets of paper. Each one cuts his sheet in a different way. Can you find the perimeter of the original sheet?

Cones and Spheres

A solid metal cone is melted down and turned into spheres. How many spheres can be made?

At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.

Half an Annulus

Can you locate the point on an annulus that splits it into two areas?

Candy Floss

What length of candy floss can Rita spin from her cylinder of sugar?

Sticky Tape

Work out the radius of a roll of adhesive tape.

Emptied Cube

Weekly Problem 26 - 2015 What are the volume and surface area of this 'Cubo Vazado' or 'Emptied Cube'?

Circle in a Semicircle

Imagine cutting out a circle which is just contained inside a semicircle. What fraction of the semi-circle will remain?

Which of these two paths made of semicircles is shorter?

Square Ratio

A square is divided into four rectangles and a square. Can you work out the ratio of the side lengths of the rectangles?

Similar Cylinders

Two similar cylinders are formed from a block of metal. What is the volume of the smaller cylinder?

Circled Corners

Three circles have been drawn at the vertices of this triangle. What is the area of the inner shaded area?

Square Flower

The diagram shows 8 circles surrounding a region. What is the perimeter of the shaded region?

Pencil Turning

Rotating a pencil twice about two different points gives surprising results...

Wood Pile Perimeter

Weekly Problem 30 - 2011 Three touching circles have an interesting area between them...

Semicircle Distance

Can you find the shortest distance between the semicircles given the area between them?

Trisected Triangle

Weekly Problem 34 - 2015 Four tiles are given. For which of them can three be placed together to form an equilateral triangle?

Rolling Inside

Weekly Problem 11 - 2007 A circle of radius 1 rolls without slipping round the inside of a square of side length 4. Find an expression for the number of revolutions the circle makes.

Square in a Circle in a Square

What is the ratio of the areas of the squares in the diagram?

Maximised Area

Of these five figures, which shaded area is the greatest? The large circle in each figure has the same radius.

Four Leaf Clover

The diagram shows four equal discs and a square. What is the perimeter of the figure?

The diagram shows a shaded shape bounded by circular arcs. What is the difference in area betweeen this and the equilateral triangle shown?

Can you find the area of the yellow part of this snake's eye?

Cut-up Square

Weekly Problem 15 - 2015 In the diagram, two lines have been drawn in a square. What is the ratio of the areas marked?

Sinking Feeling

Two vases are cylindrical in shape. Can you work out the original depth of the water in the larger vase?

Weekly Problem 51 - 2015 Charlie is making clown hats from a piece of cardboard. What is the maximum number he can make?

Can you work out the shaded area surrounded by these arcs?

Weekly Problem 5 - 2006 How many times does the inside disc have to roll around the inside of the ring to return to its initial position?

Cutting a rectangle from a corner to a point on the opposite side splits its area in the ratio 1:2. What is the ratio of a:b?

Weekly Problem 52 - 2014 Four arcs are drawn in a circle to create a shaded area. What fraction of the area of the circle is shaded?

Tilted Aquarium

Can you find the depth of water in this aquarium?

Running Race

Weekly Problem 13 - 2006 If three runners run at the same constant speed around the race tracks, in which order do they finish?

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5th Grade Volume Worksheets

Welcome to our 5th Grade Volume Worksheets page.

Here you will find our collection of worksheets to introduce and help you learn about volume.

These worksheets will help you to understand and practice how to find the volume of rectangular prisms and other simple shapes.

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Volume of Rectangular Prisms

On this webpage you will find our range of worksheets to help you work out the volume of simple 3d shapes such as rectangular prisms.

They are also very useful for introducing the concept of volume being the number of cubes that fill up a space.

These sheets are graded from easiest to hardest, and each sheet comes complete with answers.

Using these sheets will help your child to:

• learn how to find the volume of simple 3d shapes by counting cubes;
• learn how to find the volume of rectangular prisms by multiplying length x width x height
• practice using their knowledge to solve basic volume problems.

What is Volume?

• Volume is the amount of space that is inside a 3 dimensional shape.
• Because it is an amount of space, it has to be measured in cubes.
• If the shape is measured in cm, then the volume would be measured in cubic cm or cm 3
• If the shape is measured in inches, then the volume would be measured in cubic inches or in 3

Volume of a Rectangular Prism

• The volume of a rectangular prism is the number of cubes it is made from.
• To find the number of cubes, we need to multiply the length by the width by the height.
• So Volume = length x width x height or l x w x h.
• We could also multiply the area of the base (which is the length x width) by the height.
• So Volume = l x w x h or b x h (where b is the area of the base)

In the example above, the length is 3, the width is 6 and the height is 2.

So the volume is 3 x 6 x 2 = 36cm 3 or 36 cubic cm.

This tells us that there are 36 cm cubes that make up the shape.

We have split our worksheets up into different sections, to make it easier for you to select the right sheets for your needs.

• Section 1 - Find the Volume by Counting Cubes
• Section 2 - Finding the Volume by multiplication
• Section 3 - Match the Volume (multiplication)
• Section 3 - Volume Problem Solving Riddles

5th Grade Volume Worksheets - Counting Cubes

• Volume - Count the Cubes Sheet 1
• PDF version
• Volume - Count the Cubes Sheet 2

5th Grade Volume Worksheets - Find the Volume by Multiplication

The first sheet is supported, the other two sheets are more independent.

You can choose between the standard or metric versions of sheets 2 and 3 (the measurements are the same)

• Find the Volume Sheet 1 (supported)
• Find the Volume Sheet 2 (standard)
• Find the Volume Sheet 2 (metric)
• Find the Volume Sheet 3 (standard)
• Find the Volume Sheet 3 (metric)

5th Grade Volume Worksheets - Match the Volume

• Match the Volume Sheet 1
• Match the Volume Sheet 2

5th Grade Volume Worksheets - Volume Riddles

• Volume Riddles Sheet 5A
• Volume Riddles Sheet 5B

Volume of Rectangular Prisms Walkthrough Video

This short video walkthrough shows several problems from our Find the Volume Sheet 2 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, check out the video below!

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Volume of a Cube/Cuboid/Box Calculators

Each of the pages below includes a handy calculator to help you find the volume of cubes, cuboids and boxes.

• Volume of a Cube Calculator

• Volume of a Box Calculator

Converting Measures Worksheets

Here is our selection of converting units of measure for 3rd to 5th graders.

These sheets involve converting between customary units of measure and also metric units.

• Converting Customary Units Worksheets
• Metric Conversion Worksheets

5th Grade Geometry Worksheets

Here is our selection of 5th grade Geometry worksheets about angles.

The focus on these sheets is angles on a straight line, angles around a point and angles in a triangle.

• 5th Grade Geometry Missing Angles

Area Worksheets

Here is our selection of free printable area worksheets for 3rd and 4th grade.

The sheets are all graded in order from easiest to hardest.

• work out the areas of a range of rectangles;
• find the area of rectilinear shapes.
• Area Worksheets - Rectangles and Rectilinear Shapes
• Area of Right Triangles
• Area of Quadrilaterals Worksheets
• Perimeter Worksheets

Here is our selection of free printable perimeter worksheets for 3rd and 4th grade.

• work out the perimeter of a range of rectangles;
• find the perimeter of rectilinear shapes.

All the math practice worksheets in this section support Elementary Math Benchmarks.

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