The side of the isosceles trapezoid is 10cm, the large base is 17cm, and the height is 8cm. Calculate the perimeter of the trapezoid.

A trapezoid is a quadrilateral in which one pair of opposite sides is parallel, and the sides are not equal to each other.

An equilateral trapezoid is called, in which the sides are equal:

The perimeter of a trapezoid is the sum of all its sides:

P = AB + BC + CD + AD.

In order to find the perimeter of the trapezoid, you need to calculate the length of its smaller base BC.

Since the segment of the larger base located between the heights is equal to the length of the smaller base, then:

HK = BC;

AD = AН + НK + KD.

Thus:

BC = НK = AD – AН – KD.

Since the trapezoid is isosceles, then:

AH = KD.

Consider the triangle ΔАВН. To calculate AН, we use the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the legs:

AB ^ 2 = BH ^ 2 + AH ^ 2;

AH ^ 2 = AB ^ 2 + BH ^ 2;

AH ^ 2 = 10 ^ 2 – 8 ^ 2 = 100 – 64 = 36;

AH = √36 = 6 cm;

BC = НK = 17 – 6 – 6 = 5 cm.

P = 10 + 5 + 10 + 17 = 42 cm.

Answer: the perimeter of the trapezoid is 42 cm.