Area - triangles, quadrilaterals, compound shapes

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

problem

Favourite

Triangle in a trapezium

Age

11 to 16

Challenge level

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

problem

Favourite

The farmers' field boundary

Age

11 to 14

Challenge level

The farmers want to redraw their field boundary but keep the area the same. Can you advise them?

problem

Favourite

Completing quadrilaterals

Age

11 to 14

Challenge level

We started drawing some quadrilaterals - can you complete them?

problem

Favourite

Quadrilaterals in a square

Age

11 to 14

Challenge level

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

problem

Favourite

Triangles in a square

Age

11 to 14

Challenge level

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

problem

Favourite

Kite in a square

Age

14 to 18

Challenge level

Can you make sense of the three methods to work out what fraction of the total area is shaded?

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?

problem

Favourite

Growing rectangles

Age

11 to 14

Challenge level

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

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Area - triangles, quadrilaterals, compound shapes

Triangle in a trapezium

The farmers' field boundary

Completing quadrilaterals

Quadrilaterals in a square

Triangles in a square

Kite in a square

Gutter

Pick's theorem

Doesn't add up

Growing rectangles