The base of the trapezoid is 4 cm and 18 cm and the sides are 13 and 15 cm, calculate the height of the trapezoid.

| February 26, 2021 | education

From the vertices B and C of the trapezoid, we draw the heights of ВK and CH.

The larger base is divided into three sections. The sum of the segments (AK + ND) is equal to the difference between the bases (AD – BC).

AK + HD = 18 – 4 = 14 cm.

We denote the length of the segment AK through X cm, then the length of the segment НD = (14 – X) cm.

In right-angled triangles ABK and CHD, we express, according to the Pythagorean theorem, the squares of the heights ВK and CH, which are equal to each other.

ВK ^ 2 = AB ^ 2 – AK ^ 2 = 13 ^ 2 – X ^ 2 = 169 – X ^ 2.

CH ^ 2 = CD ^ 2 – DH ^ 2 = 15 ^ 2 – (14 – X) ^ 2 = 225 – 196 + 28 * X – X ^ 2 = 29 + 28 * X – X ^ 2.

Let us equate the right-hand sides of the equalities.

169 – X ^ 2 = 29 + 28 * X – X ^ 2.

28 * X = 140.

X = 140/28 = 5 cm.

ВK ^ 2 = 169 – 5 ^ 2 = 144.

ВK = 12 cm.

Answer: The height of the trapezoid is 12 cm.



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