The bases of an isosceles trapezoid are equal to 1 cm and 17 cm, and the diagonal

| May 29, 2021 | education

The bases of an isosceles trapezoid are equal to 1 cm and 17 cm, and the diagonal divides its obtuse angle in half. Find the area of the trapezoid.

Since BD is the bisector of the angle ABC, then the angle ABD = CBD.

Angle CBD = ADB as cross-lying angles at the intersection of parallel straight lines ВС and АD of secant ВD. Then the angle ABD = ADB, and then the triangle ABD is isosceles, AB = AD = 17 cm.

Since the trapezoid is isosceles, the BH height divides the larger base into two segments, the length of the smaller of which is equal to the half-difference of the base lengths.

AH = (AD – BC) / 2 = (17 – 1) / 2 = 8 cm.

Let’s build the height of the HВ.

In a right-angled triangle ABН, according to the Pythagorean theorem, BH ^ 2 = AB ^ 2 – AH ^ 2 = 289 – 64 = 225.

BH = 15 cm.

Determine the area of ​​the trapezoid.

Savsd = (ВС + АD) * ВН / 2 = (17 + 1) * 15/2 = 135 cm2.

Answer: The area of ​​the trapezoid is 135 cm2.



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