In trapezoid abcd, points m and n are arbitrary points on bases ab and cd respectively. find the area of the trapezoid, if area abn=23 cm^2 and area cdm=18 cm^2.

The locations of M and N are arbitrary, so we can choose them to make the problem easy to solve.

Let M = B. Then ∆CDM = ∆CDB = 18 cm².

Let N = D. Then ∆ABN = ∆ABD = 23 cm².

Diagonal BD divides the trapezoid into triangles ABD and CBD. The area of the trapezoid is the sum of the areas of these triangles:

... 23 cm² + 18 cm² = 41 cm² . . . . the area of the trapezoid.

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step-by-step explanation: