+704
In trapezoid $ABCD,$ $\overline{AB} \parallel \overline{CD}$. Find the area of the trapezoid.
+129850 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
