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.