The sides of a rectangular trapezoid are 5: 3, and the base difference is 32 cm.

| September 6, 2021 | education

The sides of a rectangular trapezoid are 5: 3, and the base difference is 32 cm.Find the area of the trapezoid if the smaller diagonal is 26 cm.

Let’s build the height of the CH trapezoid.

Quadrangle ABCH is a rectangle, then CH = AB, AH = BC.

Let the side length AB = 3 * X cm, then CD = 5 * X cm.

By the condition (AD – BC) = 32 cm, and since BC = AH, then (AD – AH) = 32 = DH.

In a right-angled triangle CDH, CD ^ 2 = CH ^ 2 + DH ^ 2.

25 * X ^ 2 = 9 * X ^ 2 + 1024.

16 * X ^ 2 = 1024.

X ^ 2 = 1024/16 = 64.

X = 8.

Then AB = 3 * 8 = 24 cm, CD = 5 * 8 = 40 cm.

In a right-angled triangle ABC, according to the Pythagorean theorem, BC ^ 2 = AC ^ 2 – AB ^ 2 = 676 – 576 = 100.

BC = 10 cm.

Then AD = AH + DH = 10 + 32 = 42 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * СН / 2 = (10 + 42) * 24/2 = 624 cm2.

Answer: The area of the trapezoid is 624 cm2.



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