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Question P6 Work backwards from volume or area

A square with area 100 cm²

A square has area 100 cm². Write its side length using square-root notation, then evaluate it.

A square of area 100 cm², with unknown side length.100 cm²side = ?

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About this method

Work backwards from volume or area

Use the known area or volume to find the missing measurement.

In this one. A square has equal sides. Its side length is the positive square root of its area; this is different from dividing the area by two.

Volume = base area x heightvolume360 cubic centimetreslayer60 per 1 cm; height = 6 cm

How to spot it

The question gives a cuboid's volume with two dimensions and asks for the third, or gives the volume with one length and asks for a face area. A square's area given with its side asked for belongs here too.

Common mistake

Children divide the volume by a length lying inside the face they want, instead of the length that runs into it, and get the wrong kind of measurement.

Practise a similar question

Standard A square has area 64 cm². Write its side length using square-root notation, then evaluate it.
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