# Search by Topic

Filter by: Content type:
Age range:
Challenge level:

### There are 50 results

Broad Topics > Measuring and calculating with units > Area - triangles, quadrilaterals, compound shapes ### Isometric Areas

##### Age 11 to 14 Challenge Level:

We usually use squares to measure area, but what if we use triangles instead? ### Triangles in a Square

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like? ### Gutter

##### Age 14 to 16 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area? ### Areas of Parallelograms

##### Age 14 to 16 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

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? ### Tilted Squares

##### Age 11 to 14 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

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? ### Pick's Theorem

##### Age 14 to 16 Challenge Level:

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons. ### Of All the Areas

##### Age 14 to 16 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it? ### Doesn't Add Up

##### Age 14 to 16 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

One side of a triangle is divided into segments of length a and b by the inscribed circle, with radius r. Prove that the area is: abr(a+b)/ab-r^2 ### Areas and Ratios

##### Age 16 to 18 Challenge Level:

Do you have enough information to work out the area of the shaded quadrilateral? ### Triangle Transformation

##### Age 7 to 14 Challenge Level:

Start with a triangle. Can you cut it up to make a rectangle? ### Another Triangle in a Triangle

##### Age 16 to 18 Challenge Level:

Can you work out the fraction of the original triangle that is covered by the green triangle? ### More Isometric Areas

##### Age 11 to 14 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

Can you find the areas of the trapezia in this sequence? ### Completing Quadrilaterals

##### Age 11 to 14 Challenge Level:

We started drawing some quadrilaterals - can you complete them? ### Quadrilaterals in a Square

##### Age 11 to 14 Challenge Level:

What's special about the area of quadrilaterals drawn in a square? ### Kite in a Square

##### Age 14 to 16 Challenge Level:

Can you make sense of the three methods to work out the area of the kite in the square? ### Bicentric Quadrilaterals

##### Age 14 to 16 Challenge Level:

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex. ### Maths Filler 2

##### Age 14 to 16 Challenge Level:

Can you draw the height-time chart as this complicated vessel fills with water? ### Uncanny Triangles

##### Age 7 to 11 Challenge Level:

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas? ### Shear Magic

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw? ### Biggest Enclosure

##### Age 14 to 16 Challenge Level:

Three fences of different lengths form three sides of an enclosure. What arrangement maximises the area? ### Squ-areas

##### Age 14 to 16 Challenge Level:

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. . . . ### Halving the Triangle

##### Age 16 to 18 Challenge Level:

Draw any triangle PQR. Find points A, B and C, one on each side of the triangle, such that the area of triangle ABC is a given fraction of the area of triangle PQR. ### Triangle Island

##### Age 7 to 11 Challenge Level:

You have pitched your tent (the red triangle) on an island. Can you move it to the position shown by the purple triangle making sure you obey the rules? ### Rati-o

##### Age 11 to 14 Challenge Level:

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? ### Disappearing Square

##### Age 11 to 14 Challenge Level:

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. . . . ### Overlap

##### Age 11 to 14 Challenge Level:

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. . . . ### Square Pizza

##### Age 14 to 16 Challenge Level:

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square? ### Rhombus in Rectangle

##### Age 14 to 16 Challenge Level:

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. ### Linkage

##### Age 11 to 14 Challenge Level:

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite? ### Isosceles

##### Age 11 to 14 Challenge Level:

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. ### Same Height

##### Age 14 to 16 Challenge Level:

A trapezium is divided into four triangles by its diagonals. Can you work out the area of the trapezium? ### Arrowhead

##### Age 14 to 16 Challenge Level:

The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area? ### From All Corners

##### Age 14 to 16 Challenge Level:

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. ### Kissing Triangles

##### Age 11 to 14 Challenge Level:

Determine the total shaded area of the 'kissing triangles'. ### Dividing the Field

##### Age 14 to 16 Challenge Level:

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. . . . ### Equilateral Areas

##### Age 14 to 16 Challenge Level:

ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF. ### Diagonals for Area

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio. ### Six Discs

##### Age 14 to 16 Challenge Level:

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases? ### Biggest Bendy

##### Age 16 to 18 Challenge Level:

Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area? ### At a Glance

##### Age 14 to 16 Challenge Level:

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?