Quadrilaterals 7224

In the ABCDEFGHIJKL, the two adjacent sides are perpendicular to each other, and all sides except the AL and GF sides are identical. The AL and GF parties are twice as long as the other parties. The lines BG and EL intersect at point M and divide the dodecagon into six shapes (three triangles, two quadrilaterals, and one pentagon). The EFGM square has an area of 7 cm2.

Determine the area of the other five departments.

Correct answer:

S1 =  7 cm2
S2 =  5 cm2
S3 =  2 cm2
S4 =  2 cm2
S5 =  1 cm2

Step-by-step explanation:

S6=7 cm2 S6=(1/2+1/4+1)S0  S0=S6/(1+21+41)=7/(1+21+41)=4 cm2  S0=a a a=S0=4=2 cm  S1=S(ABML) S1=S6=7=7 cm2
S2=S(CDEMB) S2=(1+1/4) S0=(1+1/4) 4=5 cm2
S3=S(JKL) S3=1/2 S0=1/2 4=2 cm2
S3=S(GIH) S4=S3=2=2 cm2
S5=S(MIJ) S5=41 S0=41 4=1 cm2

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