In trapezoid ABCD (BC || AD), points M and N divide the diagonal of BD

| September 25, 2021 | education

In trapezoid ABCD (BC || AD), points M and N divide the diagonal of BD into three equal parts. Find the area of the triangle MCN if the area of the trapezoid is 27cm ^ 2, and AD is 2p more than BC

Let’s draw the height of the HВ trapezoid.

The area of the triangle ABD is equal to: Savd = AD * BН / 2 cm2.

The area of the triangle ВСD is equal to: Sвсд = ВС * ВН / 2 cm2.

According to the condition АD = 2 * ВС, then Savd = 2 * ВС * ВН / 2 = ВС * ВН cm2.

Savsd = Savs + Svsd = 3 * ВС * ВН / 2 = 27.

ВС * ВН = 18 cm2.

Svsd = 18/2 = 9 cm2.

The triangles ВСD and МСN have the same height SK, then the ratio of their areas is equal to the ratio of their bases.

Svsd / Smsn = BD / MN = 3/1.

9 / Smcn = 3.

Smcn = 9/3 = 3 cm2.

Answer: The area of the MCN triangle is 3 cm2.



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