Area - triangles, quadrilaterals, compound shapes

There are 53 NRICH Mathematical resources connected to Area - triangles, quadrilaterals, compound shapes

problem

Favourite

Areas and ratios

Age

16 to 18

Challenge level

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

problem

Favourite

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?

problem

Favourite

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?

problem

Favourite

Areas of parallelograms

Age

14 to 16

Challenge level

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

problem

Favourite

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

problem

Favourite

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?

problem

Favourite

Twice as big?

Age

7 to 11

Challenge level

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

problem

Favourite

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?

problem

Favourite

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.

problem

Favourite

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?

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Area - triangles, quadrilaterals, compound shapes

Areas and ratios

Of all the areas

Isosceles triangles

Areas of parallelograms

So big

Trapezium four

Twice as big?

Gutter

Pick's theorem

Doesn't add up