In trapezoid ABCD, points M and N are arbitrary points on bases AB and CD respectively. Find the area of the trapezoid, if area AABN=23

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In trapezoid ABCD, points M and N are arbitrary points on bases AB and CD respectively. Find the area of the trapezoid, if area AABN=23 cm2 and area ACDM=18 cm2.

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    2021-09-10T04:26:47+00:00

    We can let M=B and N=D, so that MN becomes diagonal BD, dividing the trapezoid into ∆ABD (∆ABN) and ∆CDB (∆CDM). The sum of the areas of these triangles is the area of the trapezoid.

    area ABCD = 23 cm² +18 cm² = 41 cm²

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