The smaller base and the height of the isosceles trapezoid are 6 cm and 4 cm. The lateral side forms
| August 17, 2021 | education
The smaller base and the height of the isosceles trapezoid are 6 cm and 4 cm. The lateral side forms an angle of 60 degrees with the base. Calculate the area of the trapezoid.
In a right-angled triangle ABH, the angle BAH is 60, then tg60 = BH / AH.
AH = BH / tg60 = 4 / √3 = 4 * √3 / 3 cm.
Since trapezoid ABCD is isosceles, its height BH divides the larger base AD into two segments, the length of the smaller of which is equal to the half-difference of the lengths of its bases.
AH = (AD – BC) / 2.
2 * AH = (AD – BC).
АD = 2 * АH + ВС = 8 * √3 / 3 + 4 cm.
Determine the area of the trapezoid.
Savsd = (АD + ВС) * ВН / 2 = (8 * √3 / 3 + 4 + 4) * 4/2 = 16 * (1 + √3 / 3) cm2.
Answer: The area of the trapezoid is 16 * (1 + √3 / 3) cm2.
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