The area of a rectangular trapezoid is 120cm2, and its height is 8cm

The area of a rectangular trapezoid is 120cm2, and its height is 8cm. Find all sides of the trapezoid if one of the bases is 6cm larger than the other.

Let the smaller base of the trapezoid be equal to X cm, then, by condition, the larger base is equal to (X + 6) cm.

The area of the trapezoid is equal to: Savsd = (AD + BC) * AB / 2 = (X + 6 + X) * 8/2 = 120.

16 * X + 48 = 240.

16 * X = 192.

X = BC = 192/16 = 12 cm.

AD = 12 + 6 = 18 cm.

Let’s draw from the top С the height СН.

Segment DH = AD – BC = 18 – 12 = 6 cm.

Then, by the Pythagorean theorem, CD ^ 2 = CH ^ 2 + DH ^ 2 = 64 + 36 = 100.

СD = 10 cm.

Answer: The sides of the trapezoid are equal: 8 cm, 12 cm, 10 cm, 18 cm.