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Please refer to image for explanation.

enter image description here

Dave Kirkby
  • 551

1 Answers1

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Consider this blue triangle:

enter image description here

The area of the combined rectangle is $(a+b)h$ so the area of the large blue and red right-angled triangle is half this, namely $\frac12(a+b)h$

The area of the small rectangle on the left is $ah$ so the area of the small red right-angled triangle on the left is half this, namely $\frac12ah$

So the area of the blue triangle is the difference in area between the two right-angled triangles, namely $\frac12(a+b)h-\frac12ah = \frac12bh$, i.e. half of base times height

Henry
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  • Thank you, Henry, I haven't practised maths for a long time, and was feeling paralysed. The diagram simplifies the problem wonderfully. – Dave Kirkby Jan 19 '19 at 10:49