In triangle ABC the midpoints M and N of sides BC and AC are marked, respectively.
| February 1, 2021 | education
In triangle ABC the midpoints M and N of sides BC and AC are marked, respectively. The area of the triangle CNM is 76. Find the area of the quadrilateral ABMN.
Because M and N are the midpoints of the sides BC and AC, then MN is the middle line parallel to the side AB. It is known that the middle line cuts off a triangle similar to the original, and the area of the cut off triangle is equal to one fourth of the area of this triangle. Therefore, triangles ABC and CMN are similar, and the area of triangle ABC is four times the area of triangle CMN and is equal to 76 * 4 = 304.
The area of the quadrilateral ABMN is equal to the difference between the areas of triangles ABC and CMN: 304 – 76 = 228.
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