ABCD – Rectangular trapezoid, AC = diagonal, 20 cm. CD = 16√2, D = 45 degrees. Find P, S of trapezoid ABCD.

| September 7, 2021 | education

In a right-angled triangle СDН, one of the acute angles is 45, then the second acute angle is also 45, and therefore the triangle СDН is isosceles, СН = DH.

Sin45 = CH / CD.

СН = DH = СD * Sin45 = 16 * √2 * √2 / 2 = 16 cm.

From the right-angled triangle ASN, by the Pythagorean theorem, we determine the length of the leg AN.

AH ^ 2 = AC ^ 2 – CH ^ 2 = 400 – 256 = 144.

AH = 12 cm.

Since the quadrangle ABCN is a rectangle, then AB = CH = 16 cm, BC = AH = 12 cm.

Let’s define the perimeter of the trapezoid.

Ravsd = AB + BC + CD + AD = 16 + 12 + 16 * √2 + 28 = 56 + 16 * √2 cm.

Determine the area of ​​the triangle.

Savsd = (ВС + АD) * СН / 2 = (12 + 28) * 16/2 = 320 cm2.

Answer: The perimeter of the trapezoid is 56 + 16 * √2 cm, the area of ​​the trapezoid is 320 cm2.



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