The height drawn from the apex of an obtuse angle of a rectangular trapezoid divides it into a square and a triangle.

| March 11, 2021 | education

The height drawn from the apex of an obtuse angle of a rectangular trapezoid divides it into a square and a triangle. The area of the triangle is 16cm2, the acute angle of the trapezoid is 45 degrees Find the area of the trapezoid.

CH – the height of the trapezoid, then the triangle CDH is rectangular, and since the angle ADC = 45, then this triangle is also isosceles, CH = CD.

The area of the triangle СDН is equal to: Sсдн = СН * DH / 2 = СН ^ 2/2.

Then CH ^ 2 = 2 * Ssdn = 2 * 16 = 32.

CH = DH = 4 * √2 cm.

Since, by condition, ABCH is a square, then AB = BC = AN = CH = 4 * √2 cm.

AD = AN + DH = 2 * DH = 2 * 4 * √2 = 8 * √2 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * СН / 2 = (4 * √2 + 8 * √2) * 4 * √2 / 2 = 48 cm2.

Answer: The area of the trapezoid is 48 cm2.



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