# The bases of an isosceles trapezoid are 2 and 11, and the perimeter is 28. Find the area of the trapezoid.

October 8, 2021 | education

| Knowing the perimeter of the isosceles trapezoid and its base, we find the lateral side AB = CD:

(28 – 2 – 11) / 2 = 7.5.

Now we find AE = FD: (AD – BC) / 2 = (11 – 2) / 2 = 4.5.

The ABE triangle is rectangular. By the Pythagorean theorem, we find BE:

BE ^ 2 = AB ^ 2 – AE ^ 2;

BE ^ 2 = 56.25 – 20.25 = 36.

BE = 6.

The area of the trapezoid is equal to the half-sum of the bases, multiplied by the height:

S = (AD + BC) / 2 * BE = (11 + 2) / 2 * 6 = 13/2 * 6 = 39.

Answer: the area of the trapezoid is 39.

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