Find the square of the area of an isosceles trapezoid if its perimeter is 10, its acute angle is 60 °, and the base difference is 2.

| January 4, 2021 | education

Let’s draw the heights of the BH and CK of the trapezoid By condition, the base difference is 2 cm, then AH + DK = 2 cm, and since the trapezoid is isosceles, then AH = DH = 2/1 = 1 cm.
In a right-angled triangle ABH, the angle ВAН = 600, then the angle ABН = 180 – 90 – 60 = 300. The leg AН lies opposite the angle 300, then the hypotenuse AB = 2 * BH = 2 * 1 = 2 cm.
Determine the height of the HВ. ВН = AB * Sin60 = 2 * √3 / 2 = √3 cm.
Let the length of BC = X cm, then НK = X cm, and AD = X + 2 cm.
By condition, the perimeter of the trapezoid is 10 cm. P = 10 = AB + BC + CD + AD = 2 + X + 2 + (X + 2).
2 * X = 10 – 6 = 4.
X = BC = 4/2 = 2 cm.
BP = 2 + 2 = 4 cm.
Determine the area of ​​the trapezoid.
S = (BC + AD) * BH / 2 = (2 + 4) * √3 / 2 = 3 * √3 cm2.
Then S ^ 2 = (3 * √3) ^ 2 = 27 cm4.
Answer: The square of the area is 27 cm4.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.