Find the height of the trapezoid if its bases are 18 cm and 24 cm, and the area is 210 cm ^ 2.
| June 23, 2021 | education
The area of the trapezoid is equal to the product of its height by the length of the midline: S = h * m, where h is the height, m is the midline. Therefore, the height of the trapezoid can be determined by dividing the area value by the length of the center line: h = S / m.
The middle line of a trapezoid is equal to half the sum of the lengths of its bases: m = (a + b) / 2.
By condition, the bases of the trapezoid are 18 and 24 cm, which means the middle line is equal to:
m = (18 + 24) / 2 = 42/2 = 21 cm.
The desired height of the trapezoid: h = S / m = 210/21 = 10 cm.
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