Square equal rhombus

Construct a square that has the same area as a rhombus ABCD if |AB| = 5cm, |AD| = 4cm and angle |DAB| = 30°.

Correct answer:

a =  3.1623 cm

Step-by-step explanation:

1;AB; ∣AB∣=5cm 2;∢ ∠XAB, ∢ ∠XAB = 30° 3;k1​;k1​(A,r=∣AD∣=4cm) 4;D; D = k1​∩XA 5;ABCD 6; p; p = AB 7; Y; Y ∈p; BY=v(AB,CD) 8; S; S∈p; ∣AS∣=∣YS∣ 9; k2​;k2​(S,r2​=AS) 10; p2​;p2​ ⊥ p; B∈ p2​ 12; Z; Z = p2​∩k2​ 13; a = ∣ZB∣ 14; EFGH; ∣EF∣=∣FG∣=∣GH∣=∣HE∣=a  AB=5 cm α=30 ∘ AD=4 cm  v=AD⋅ sin(α)=4⋅ sin(30°)=2 cm  a2 = AB⋅ v a=AB⋅ v​=5⋅ 2​=10​≐3.1623 cm   Verifying Solution:  S1​=AB⋅ v=5⋅ 2=10 cm2 S2​=a2=3.16232=10 cm2

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