Start with a triangle. Can you cut it up to make a rectangle?
Determine the total shaded area of the 'kissing triangles'.
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.
Isometric Areas explored areas of parallelograms in triangular units. Here we explore areas of triangles...
We usually use squares to measure area, but what if we use triangles instead?
What are the possible areas of triangles drawn in a square?
We started drawing some quadrilaterals - can you complete them?
What's special about the area of quadrilaterals drawn in a square?
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?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
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. . . .
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. . . .
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?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
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?
What happens to the area and volume of 2D and 3D shapes when you enlarge them?
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?
Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?