The sides of the trapezoid are 7 cm and 13 cm, and the middle line is 14.

| April 25, 2021 | education

The sides of the trapezoid are 7 cm and 13 cm, and the middle line is 14. Find the perimeter and area of the trapezoid if the angle B = 135 °

From the top B of the trapezoid, we draw the height ВН.

In a right-angled triangle ABН, the angle ABН = ABC – СВН = 135 – 90 = 45.

Then the angle ВAН = 180 – 90 – 45 = 45, and therefore the triangle AВН is isosceles, AH = BH.

Then Sin45 = HВ / AB.

ВН = AB * Sin45 = 7 * √2 / 2 cm.

Since the middle line of the trapezoid is equal to the half-sum of the bases, the area of ​​the trapezoid is equal to: Savsd = KR * ВН = 14 * 7 * √2 / 2 = 49 * √2 cm2.

Let us determine the sum of the lengths of the bases of the trapezoid. KP = 14 = (BC + AD) / 2.

BC + AD = 2 * 14 = 28 cm.

Then the perimeter of the trapezoid is: Ravsd = AB + CD + BC + AD = 7 + 13 + 28 = 48 cm.

Answer: The area of ​​the trapezoid is 49 * √2 cm2, the perimeter of the trapezoid is 48 cm.



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