Find the area of an isosceles trapezoid, the smaller base of which is 7 cm, the lateral side is 10 cm

Find the area of an isosceles trapezoid, the smaller base of which is 7 cm, the lateral side is 10 cm and the angle for the larger base is 60 degrees.

An isosceles trapezoid is a trapezoid in which the corresponding angles at the base are equal, and the sides are equal.

Consider a triangle ABН formed by the height of the ВН.

Using the cosine theorem, we can find the length of the segment AH:

cos A = AH / AB;

cos 60 ° = ½;

AH = AB · cos A;

AH = 10 0.5 = 5 cm.

Now we find the height of the VN behind the Pythagorean theorem:

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

BH ^ 2 = AB ^ 2 – AH ^ 2;

BH ^ 2 = 10 ^ 2 – 5 ^ 2 = 100 – 25 = 75;

BH = √75 = 8.66 cm.

Find the length of the bottom base. Since the trapezoid is isosceles, the segments AH and KD are equal, thus:

AD = BC + AH + KD;

AD = 7 + 5 + 5 = 17 cm.

The area of ​​the trapezoid is equal to the product of the half-sum of its bases by the height:

S = (BC + AD) / 2 * BH;

S = (7 + 17) / 2 * 8.66 = 103.92 cm2.

Answer: the area of ​​the trapezoid is 103.92 cm2.