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Prove that the area of a trapezium is half the sum of the parallel sides multiplied by thedistance between them.7. |
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Answer» Draw a trapezium say abcd and join the diagonals you will obtain two triangle draw two perpendiculars on diagonals from both parallel sidesnow area of quadrilateral(trapezium)=sum of area of both the triangles let a and b be two parallel sides and h be the perpendicularsarea of 1st triangle=1/2 x a x h ....1area of 2nd triangle=1/2 x b xh .........2 sum of 1 and 2 = area of quadrilateral(trapezium)1/2 x a x h +1/2 x b xh= area of trapezium 1/2 x (a+b) x h= area of trapezium (taking out 1/2 as common) thus proved............ |
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