In isosceles trapezoid ABCD, the degree measure of angle A is three times less than the degree measure of angle B

| April 9, 2021 | education

In isosceles trapezoid ABCD, the degree measure of angle A is three times less than the degree measure of angle B and BC parallel to AD. The segments BF and CP are the heights of the trapezoid. The side length of the square FBCP is 10 cm. Calculate the area of the trapezoid, the bases of which are the middle line and the smaller base of the trapezoid ABCD.

Let the value of the angle BAD = X0, then, by condition, the angle ABC = 3 * X0.

The sum of the angles of the trapezoid at the side is 180, then (X + 3 * X) = 180.

4 * X = 180.

X = 180/4 = 45.

Angle BAD = 45, angle ABC = 3 * 45 = 135.

The right-angled triangle ABF is isosceles, since the angles at the base of AB are equal to 45, then AF = BF = 10 cm, since the BDPC is a square with a side of 10 cm. The segment DP = AF = 10 cm, since the trapezoid is isosceles. Then АD = AF + FP + РD = 10 + 10 + 10 = 30 cm.

Determine the length of the center line of the CM.

KM = (BC + AD) / 2 = (10 + 30) / 2 = 40/2 = 20 cm.

Determine the area of ​​the trapezium KВСM.

Skvcm = (ВС + KM) * ВН / 2 = (10 + 20) * 5/2 = 150/2 = 75 cm2.

Answer: The area of ​​the KВСM trapezoid is 75 cm2.



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