Trapezoid MO

The rectangular trapezoid ABCD with the right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other.

Calculate the perimeter and area of the trapezoid.

Correct answer:

o = 33.31
S = 69.25

Step-by-step explanation:

A C = 12 C D = 8 sin Φ = \frac{∣ B C ∣}{∣ A C ∣} cos Φ = \frac{∣ B C ∣}{∣ B D ∣} cos^{2} Φ + \frac{∣ C D ∣}{∣ A C ∣} cos Φ - 1 = 0 x^{2} + C D / A C \cdot x - 1 = 0 x^{2} + 8 / 12 \cdot x - 1 = 0 x^{2} + 0.667 x - 1 = 0 a = 1; b = 0.667; c = - 1 D = b^{2} - 4 a c = 0.66 7^{2} - 4 \cdot 1 \cdot (- 1) = 4.4444444444 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 0 . 6 7 \pm 4 . 4 4}{2} x_{1, 2} = - 0.333333 \pm 1.054093 x_{1} = 0.72075922 x_{2} = - 1.387425887 x = x_{1} = 0.7208 ≐ 0.7208 Φ = arccos x = arccos 0.7208 ≐ 0.7659 rad Φ_{2} = Φ \to ° = Φ \cdot \frac{1 8 0}{π} ° = 0.7659 \cdot \frac{1 8 0}{π} ° = 43.8828 ° B C = A C \cdot sin (Φ) = 12 \cdot sin 0.7659 ≐ 8.3182 A B = A C \cdot cos (Φ) = 12 \cdot cos 0.7659 ≐ 8.6491 A D = B C^{2} + (A B - C D)^{2} = 8.318 2^{2} + (8.6491 - 8)^{2} ≐ 8.3435 o = A B + B C + C D + A D = 8.6491 + 8.3182 + 8 + 8.3435 = 33.31

Our quadratic equation calculator calculates it.

S = \frac{( A B + C D ) \cdot B C}{2} = \frac{( 8 . 6 4 9 1 + 8 ) \cdot 8 . 3 1 8 2}{2} = 69.25

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Math student

How do you find the answer

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