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

Question

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.

0

Answers ( No )

    0
    2021-09-10T08:03:15+00:00

    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.

Leave an answer

Browse
Browse