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Resources tagged with Area - triangles, quadrilaterals, compound shapes similar to Making Rectangles:

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

Age 11 to 14 Challenge Level:

We started drawing some quadrilaterals - can you complete them?

Growing Rectangles

Age 11 to 14 Challenge Level:

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

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?

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?

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?

Isometric Areas

Age 11 to 14 Challenge Level:

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

Triangle Transformation

Age 7 to 14 Challenge Level:

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

Kissing Triangles

Age 11 to 14 Challenge Level:

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

Pick's Theorem

Age 11 to 14 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.

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.

Triangles in a Square

Age 11 to 14 Challenge Level:

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

More Isometric 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:

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?

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?

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?

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?

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. . . .

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. . . .

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?

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?