Calculate 5

Calculate the area and perimeter of a trapezoid with side a = 10, angle α = 40°, angle β = 50°, and side c = 3.

Final Answer:

S = 22.4044
o = 22.8618

a = 10 c = 3 α = 40^{\circ} β = 50^{\circ} w = a - c = 10 - 3 = 7 tan α = h : x tan β = h : y x + y = w x tan α = h y tan β = h x tan α = y tan β r = \frac{tan α}{tan β} = \frac{tan 4 0 °}{tan 5 0 °} = \frac{0 . 8 3 9 1}{1 . 1 9 1 7 5 4} = 0.70409 x \cdot r = y x \cdot r = w - x x \cdot 0.70408819104185 = 7 - x 1.704088 x = 7 x = \frac{7}{1 . 7 0 4 0 8 8 1 9} = 4.10776862 x = 4.107769 y = w - x = 7 - 4.1078 ≐ 2.8922 h = x \cdot tan α = x \cdot tan 40 ° = 4.1078 \cdot tan 40 ° = 4.1078 \cdot 0.8391 = 3.44683 S = \frac{a + c}{2} \cdot h = \frac{1 0 + 3}{2} \cdot 3.4468 = 22.4044

sin α = h : d d = \frac{h}{sin α} = \frac{h}{sin 4 0 °} = \frac{3 . 4 4 6 8}{sin 4 0 °} = \frac{3 . 4 4 6 8}{0 . 6 4 2 7 8 8} = 5.36231 sin β = h : b b = \frac{h}{sin β} = \frac{h}{sin 5 0 °} = \frac{3 . 4 4 6 8}{sin 5 0 °} = \frac{3 . 4 4 6 8}{0 . 7 6 6 0 4 4} = 4.49951 o = a + b + c + d = 10 + 4.4995 + 3 + 5.3623 = 22.8618

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