How to show the formula for the area of a trapezium

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A one-minute video showing you how to prove that the area of trapezium = sum of the parallel sides x height / 2.

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WHAT YOU NEED: A ruler, pens, scissors and paper.
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STEP 1 - TRAPEZIUM x 2: On a rectangular piece of paper, use a ruler to draw two angled lines from the bottom corners to make a trapezium shape. Then cut along these lines with the scissors to make your trapezium...
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...use the ruler and a coloured felt tip pen to draw a line along the bottom edge of the trapezium, then use another colour to draw a line along the top edge. These are the two parallel sides of the trapezium....
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...place the trapezium on the second piece of card and draw around the outline. Cut along the lines with the scissors. You should now have two identical trapeziums...
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...draw coloured lines along the top and bottom edges of the second trapezium to match the first one.
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STEP 2 - MAKE PARALLELOGRAM: Rotate the second trapezium by 180 degrees and line it up with the first to make a parallelogram.
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STEP 3 - MAKE RECTANGLE: At one end of the parallelogram, use the ruler to draw from the bottom corner a line that is perpendicular - that's at a right angle - to the parallel sides. Cut along the line...
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...then place the right-angled triangle you cut off at the other end of the trapezium to make a rectangle. The area of a rectangle is base x height. Here the base is the sum of the parallel sides of the original trapezium. The blue + orange lengths.
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STEP FOUR - 1 TRAPEZIUM = ½ RECTANGLE: This rectangle has the same area as TWO trapeziums. So the area of ONE trapezium must be HALF the area of the rectangle. So that's half the sum of the parallel sides x height. You've done it!

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How to show the formula for the area of a trapezium

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