# Find the area of an isosceles trapezoid in which the bases are 42cm and 54cm

Find the area of an isosceles trapezoid in which the bases are 42cm and 54cm, and the angle for a large base is 45 degrees.

1. The tops of the trapezoid – A, B, C, D. AD = 54 cm. BC = 42 cm. BH – height (drawn to AD).

S is the area of the trapezoid. ∠А = 45 °.

2. The length of the segment АН is calculated by the formula: АН = (АD – ВС) / 2 (according to the properties isosceles trapezoid).

AH = (54 – 42) / 2 = 6 cm.

3. We calculate the length of the height BH through the tangent ∠A, which is equal to the quotient of dividing the leg BH by the leg AH.

BH: AH = tangent ∠A = tangent 45 ° = 1.

BH = AH x 1 = 6 x 1 = 6 cm.

4. S = (АD + ВС) / 2 х ВН = (54 + 42) / 2 х 6 = 288 cm².

Answer: S is equal to 288 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.