In an even-sided trapezoid, the upper base is 60 cm, the height is 12 cm, the lateral side forms an angle

| March 9, 2021 | education

In an even-sided trapezoid, the upper base is 60 cm, the height is 12 cm, the lateral side forms an angle of 60 degrees with the lower base. Find the bottom base of the trapezoid.

In the right-angled triangle ABН, we determine the length of the leg AH.

Tg60 = ВН / AH.

AH = BH / tg60 = 12 / √3 = 4 * √3 cm.

Let us draw the height of the CК from the vertex C of the trapezoid. Triangle ABН and CDK are equal in hypotenuse and acute angle, since AB = СD as lateral sides of an isosceles trapezium, angle A = D as angles at the base. Then DH = AН.

Quadrangle ВСKН is a rectangle, since ВН and СK are perpendicular to the bases of the trapezoid, then НK = BC = 60 cm.

Determine the length of the larger base. AD = AH + НK + DK = 4 * √3 + 60 + 4 * √3 = 60 + 8 * √3 cm.

Answer: The length of the larger base is 60 + 8 * √3 cm.



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