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In trapezoid $ABCD,$ $\overline{AB} \parallel \overline{CD}$. Find the area of the trapezoid.
 

 

 Mar 9, 2024
 #1
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Angle BDC   = 30

 

To find base CD

CD / sin DBC  = BC / sin BDC

CD / sin 80  = 6 / sin 30

CD  = 6 * sin 80  / sin 30  =  6 * sin 80 / (1/2)  =  12sin(80)

 

Area of triangle BDC =

(1/2) BC * CD * sin 70  =

(1/2) 6 * 12sin 80 * sin70 =

36sin 80 * sin 70  ≈  33.3

 

To find BD

BD /sin70 = BC / sin30

BD /sin70 = 6 / (1/2)

BD / sin70 = 12

BD = 12sin70

 

Area of triangle ABD

(1/2) AB *BD sin ABD =

(1/2) *3 * 12sin (70)*sin (30)  =

18 sin (70) * (1/2) =

9 sin (70)  ≈ 8.46

 

Area of trapezoid  =  Area of triangle BDC + Area of triangle ABD  = 

33.3  + 8.46 ≈  41.76

 

cool cool cool

 Mar 9, 2024

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