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### Number and algebra

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### Working mathematically

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### For younger learners

# Areas from Vectors

*This resource is part of "Dotty Grids - Exploring Coordinates and Vectors"*

Is there a formula for the area of a parallelogram if I know the two vectors?

Why does the formula work?

What is the formula in the special case when the parallelogram is a square?

What is special about the areas of the rhombuses you can make?

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Age 11 to 16

Move the blue points below to change the vectors that define the parallelogram.

See how the area changes.

Explore how the area of the parallelogram changes as you change the vectors.

If you would like some ideas of interesting questions to explore, take a look below.

Is there a formula for the area of a parallelogram if I know the two vectors?

Why does the formula work?

What is the formula in the special case when the parallelogram is a square?

What is special about the areas of the rhombuses you can make?

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?