### There are 20 results

Broad Topics >

Measuring and calculating with units > Area - triangles, quadrilaterals, compound shapes

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

Start with a triangle. Can you cut it up to make a rectangle?

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

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

##### 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.

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

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

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

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

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

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

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

We started drawing some quadrilaterals - can you complete them?

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

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

##### 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?

##### 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?

##### 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. . . .

##### 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. . . .

##### 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?

##### 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?

##### 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?

##### 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?

##### 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?

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

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

##### 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?

##### 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?