In an isosceles trapezoid A1A2A3A4, the lateral side is 60 mm, and the bases are 90 mm and 18 mm.

In an isosceles trapezoid A1A2A3A4, the lateral side is 60 mm, and the bases are 90 mm and 18 mm. Find the height of the trapezoid.

Let’s draw the heights А2Н and А3К of the trapezoid.

Since the trapezoid is isosceles, then A1A2 = A3A4, and the angle A2A1A4 = A3A4A1. Then right-angled triangle A1A2H is equal to right-angled triangle A3A4K in hypotenuse and acute angle, then A1H = A4K.

Rectangle HA2A3K is a rectangle, since A1H and A3K are perpendicular to the bases, then HK = A2A3 = 18 mm.

A1H = A4K = (A1A4 – A2A3) / 2 = (90 – 18) / 2 = 36 mm.

From the right-angled triangle A1A2H, we determine the length of the leg A2H.

A2H ^ 2 = A1A2 ^ 2 – A1H ^ 2 = 60 ^ 2 – 36 ^ 2 = 3600 – 1296 = 2304.

A2H = 48 mm.

Answer: The height of the trapezoid is 48 mm.