In a rectangular trapezoid, one of the angles is 135 degrees, the middle line is 18 cm, and the bases are 1: 8.

| January 30, 2021 | education

In a rectangular trapezoid, one of the angles is 135 degrees, the middle line is 18 cm, and the bases are 1: 8. Calculate: the base of the trapezoid and the area of the trapezoid.

Since the bases are 1: 8, we denote the smaller base as x, and the larger one – 8x.

The middle line is equal to the half-sum of the bases: (x + 8x) / 2 = 18; 9x = 36; x = 4 (cm) – smaller base of the trapezoid. Then the larger base is 8x = 8 * 4 = 32 (cm).

Let’s calculate the value of the acute angle of the trapezoid: 180 ° – 135 ° = 45 °.

Drop the height from the obtuse angle of the trapezoid (which is 135 °). It will cut off an isosceles triangle from the trapezoid (one angle is straight, the second is 45 °, which means that the third angle is 45 °). Therefore, the height of the trapezoid is equal to the difference between the bases: the height is 32 – 4 = 28 (cm).

We calculate the area of ​​the trapezoid (it is equal to the product of the midline and the height):

S = 18 * 28 = 504 (cm²).

Answer: the bases of the trapezoid are 4 cm and 32 cm, the area is 504 cm².



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