Find the area of an equilateral trapezoid with bases of 10 cm and 18 cm, if its lateral side

| January 5, 2021 | education

Find the area of an equilateral trapezoid with bases of 10 cm and 18 cm, if its lateral side forms a greater main angle of 60 degrees

The length of the larger base of any trapezoid is equal to the sum of the lengths of the smaller base and the projections of the lateral sides onto the larger base. Since this trapezoid is isosceles, its sides are equal, hence their projections are also equal. The size of the projection of the side can be found by dividing the difference in the lengths of the bases by two: (18 – 10) / 2 = 8/2 = 4 cm.
Consider a right-angled triangle formed by the height of the trapezoid, the lateral side and its projection. The height and projection are the legs, and the height is the leg, opposite to the angle between the lateral side and the large base, equal to 60 °, the projection of the lateral side is the leg adjacent to this angle.
The ratio of the opposite leg to the adjacent leg is the tangent of the angle, which means:
h / 4 = tg 60 °;
h = 4 * tg 60 ° = 4√3 cm.
The area of ​​the trapezoid is defined as the product of the height and half the sum of the lengths of the bases:
S = 4√3 * (10 + 18) / 2 = 2√3 * 28 = 56√3 ≈ 97 cm2.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.