Lessons · Teaching · perimeter and area
Perimeter is a length; area is a covering
Perimeter is the distance round the edge, measured in units of length. Area is the number of unit squares that cover the surface, measured in square units. They are different kinds of quantity and no amount of one tells you the other.
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In beta. This lesson was written for Hone and has not yet been checked by a state certification officer. Practice material, not professional advice. What that means.
What it is for
Two rectangles with the same perimeter can have very different areas, and that is the lesson worth making a pupil discover: 1 by 11 and 6 by 6 both have a perimeter of 24, and their areas are 11 and 36. A teacher who has that example ready can end the confusion in one minute.
How to think about it
Ask what is being measured: a fence or a lawn? A fence is a length, so add the sides. A lawn is a covering, so multiply. For an odd shape, break it into rectangles for area, but walk the whole outside for perimeter.
Worked example
A rectangle 8 by 5: perimeter is 2(8 + 5) = 26 unitsTwo lengths and two widths. Adding 8 and 5 alone is half a fence.
Its area is 8 x 5 = 40 square unitsForty unit squares cover it. The unit is squared because two lengths were multiplied.
A triangle's area is half the base times the height: a 10 by 6 triangle is 30Half of the rectangle it sits inside. The height is perpendicular, not a sloping side.
Same perimeter, different area: 1x11 and 6x6 both fence at 24, and cover 11 and 36The example that makes the distinction stick.
Your turn
Name the unit kind that area is always measured in.
Area is measured in units
Solve one, graded on the server
The trap
Using a sloping side as the height of a triangle. The height is the perpendicular distance from the base to the opposite point, and on an obtuse triangle it can fall outside the shape entirely.