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

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.

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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

Areas of parallelograms

So big

Trapezium four

Twice as big?