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Resources tagged with Area similar to Doesn't Add Up:

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Broad Topics > Measures and Mensuration > Area

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Doesn't Add Up

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

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Muggles Magic

Stage: 3 Challenge Level: Challenge Level:1

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

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Framed

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .

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Efficient Packing

Stage: 4 Challenge Level: Challenge Level:1

How efficiently can you pack together disks?

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Lying and Cheating

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!

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Dissect

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

It is possible to dissect any square into smaller squares. What is the minimum number of squares a 13 by 13 square can be dissected into?

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From All Corners

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

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Poly-puzzle

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

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Shear Magic

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

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Disappearing Square

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

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Of All the Areas

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

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Gutter

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

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Two Circles

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Draw two circles, each of radius 1 unit, so that each circle goes through the centre of the other one. What is the area of the overlap?

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Warmsnug Double Glazing

Stage: 3 Challenge Level: Challenge Level:1

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

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Diagonals for Area

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you prove this formula for finding the area of a quadrilateral from its diagonals?

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Isosceles Triangles

Stage: 3 Challenge Level: Challenge Level:1

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?

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Bound to Be

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Four quadrants are drawn centred at the vertices of a square . Find the area of the central region bounded by the four arcs.

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Growing Rectangles

Stage: 3 Challenge Level: Challenge Level:1

What happens to the area and volume of 2D and 3D shapes when you enlarge them?

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Appearing Square

Stage: 3 Challenge Level: Challenge Level:1

Make an eight by eight square, the layout is the same as a chessboard. You can print out and use the square below. What is the area of the square? Divide the square in the way shown by the red dashed. . . .

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Tiling Into Slanted Rectangles

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A follow-up activity to Tiles in the Garden.

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Uniform Units

Stage: 4 Challenge Level: Challenge Level:1

Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?

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Covering Cups

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

What is the shape and dimensions of a box that will contain six cups and have as small a surface area as possible.

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Bicentric Quadrilaterals

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.

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Extending Great Squares

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Explore one of these five pictures.

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Overlap

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

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Tilted Squares

Stage: 3 Challenge Level: Challenge Level:1

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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Inscribed in a Circle

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?

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Rati-o

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

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Fence It

Stage: 3 Challenge Level: Challenge Level:1

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

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Max Box

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Three rods of different lengths form three sides of an enclosure with right angles between them. What arrangement maximises the area

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Isosceles

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.

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An Unusual Shape

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you maximise the area available to a grazing goat?

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Percentage Unchanged

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) is the width decreased by ?

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Pie Cuts

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).

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The Pillar of Chios

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Semicircles are drawn on the sides of a rectangle ABCD. A circle passing through points ABCD carves out four crescent-shaped regions. Prove that the sum of the areas of the four crescents is equal to. . . .

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Dividing the Field

Stage: 4 Challenge Level: Challenge Level:1

A farmer has a field which is the shape of a trapezium as illustrated below. To increase his profits he wishes to grow two different crops. To do this he would like to divide the field into two. . . .

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Two Shapes & Printer Ink

Stage: 4 Challenge Level: Challenge Level:1

If I print this page which shape will require the more yellow ink?

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Quadarc

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the. . . .

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Same Height

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

A trapezium is divided into four triangles by its diagonals. Suppose the two triangles containing the parallel sides have areas a and b, what is the area of the trapezium?

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Kissing Triangles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Determine the total shaded area of the 'kissing triangles'.

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Square Pegs

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

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Take Ten

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3. . . .

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Cylinder Cutting

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.

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Areas of Parallelograms

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find the area of a parallelogram defined by two vectors?

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Square Areas

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you work out the area of the inner square and give an explanation of how you did it?

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Compare Areas

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?

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Rhombus in Rectangle

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.

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Partly Circles

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the same and what is different about these circle questions? What connections can you make?

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Squ-areas

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Three squares are drawn on the sides of a triangle ABC. Their areas are respectively 18 000, 20 000 and 26 000 square centimetres. If the outer vertices of the squares are joined, three more. . . .

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Curvy Areas

Stage: 4 Challenge Level: Challenge Level:1

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?