#In the diagram, there is a parallelogram ABCD, where 𝐡𝐸=𝐸𝐢=𝐹𝐷. Find the area

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topaz flint
rotund socketBOT
topaz flint
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In the diagram, there is a parallelogram ABCD, where 𝐡𝐸=𝐸𝐢=𝐹𝐷. Find the area of triangle 𝐡𝐸𝑀. BEM, if the area of parallelogram 𝐴𝐡𝐢𝐸
ABCE is 72.

raven wharf
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hmmm, ABCE is no parallellogram. Did you mean area of AECF is 72 or is it ABCD? In any case, similarity is the key I would say.

light shale
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I got 6

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||First I used vertical angle theorem, triangle congruency, and angle sum theorems to prove AMD and EMB similar. Then I found half of AD is equal to BE, so the other sides must follow.
After that i used the fact the two times side length is four times area for the area to create the next equitation.
If you slide CFD and ABE towards each other you find they add up to half of the area of the entire parallelogram (72 => 36).
You can also see that BD cuts the parallelogram in half so the triangles that are made from that must be equal to each other and equal half of the area of the entire parallelogram (72 => 36).
You can also see that BEM and BAM combine to make the triangle when we combined with the other triangle earlier, made half of the area of the parallelogram. So BRM and BAM must be half of the half of the area of the parallelogram (18).
MAD and BAM also make up the triangle that is half of the area of the parallelogram.
Using this we can create a system of equations to solve for BEM. || sorry I’m not that good at explaining

umbral jacinth
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Another solution: S(BME)=1/6*S(BCD)=6, p.s: BM=MN=ND due to mass center th.