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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?
The farmers want to redraw their field boundary but keep the area the same. Can you advise them?
Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?
We started drawing some quadrilaterals - can you complete them?
What's special about the area of quadrilaterals drawn in a square?
What are the possible areas of triangles drawn in a square?
What happens to the area and volume of 2D and 3D shapes when you enlarge them?
Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?
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?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?
This task challenges you to create symmetrical U shapes out of rods and find their areas.
Start with a triangle. Can you cut it up to make a rectangle?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
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?
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?
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?
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. Do you have any interesting findings to report?
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?
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.
Determine the total shaded area of the 'kissing triangles'.