The distance from the middle of the larger base of the isosceles trapezoid to the apex of the obtuse angle

| September 11, 2021 | education

The distance from the middle of the larger base of the isosceles trapezoid to the apex of the obtuse angle is equal to the smaller base, and the larger base is 2 times greater than the smaller one. Calculate the perimeter of the trapezoid if the length of the smaller base is 12cm.

Given:

ABCD is an isosceles trapezoid.

E is the middle of the larger AD base.

BC = BE.

BC = 1/2 AD = 12 centimeters.

Solution:

BC || BE; BC = BE – by condition, therefore, EBCD is a parallelogram (opposite sides are equal and parallel).

Therefore BE = CD. CD is the side of the trapezoid. Since the trapezoid ABCD is isosceles by the condition, the lateral side CD = the lateral side AB = BE = BC = 1/2 AD = 12 centimeters.

Find the length of the larger base AD if it is 2 times longer than the smaller base BC:

12 * 2 = 24 (centimeters) – the larger base of the trapezoid.

The perimeter of a trapezoid is the sum of all its sides. Let’s write the formula:

P = a + a + b + b = 2a + 2b = 2 * (a + b).

Thus:

P = AB + BC + CD + DA = 12 + 12 + 12 + 24 = 60 (centimeters).

Answer: 60 centimeters.



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