Maths · Geometry and measures. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
Congruent shapes are exactly the same shape and the same size. One could be placed on top of the other, perhaps after a turn or a flip. For triangles you do not need to check everything: four short tests are enough.
Similar shapes are the same shape but a different size. All matching angles are equal and all matching lengths are multiplied by the same number, called the scale factor. To find a missing length, find the scale factor from a pair of matching sides, then multiply or divide.
When lengths are multiplied by k, areas are multiplied by k2 and volumes by k3. This is because area uses two lengths multiplied together and volume uses three.
Using the length scale factor for an area or a volume. If the lengths are 3 times as big, the area is 9 times as big and the volume is 27 times as big, not 3 times.
Answer: 63 cm2
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