ABCD is an isosceles trapezoid. Diagonal AC = 100 mm, height AO = 60 mm, OB = 45 mm. Find the area of the trapezoid.

In a right-angled triangle AOС, according to the Pythagorean theorem, we determine the length of the leg OС.

OС ^ 2 = AC ^ 2 – OA ^ 2 = 100 ^ 2 – 60 ^ 2 = 10000 – 3600 = 6400.

OС = 80 mm.

Determine the length of the BC base. BC = OC – ОВ = 80 – 45 = 35 mm.

Let’s draw the heights of the ВН and СK to the larger base of the AD. Since the trapezoid is isosceles, then AH = DK.

AH = OВ = 45 mm, since OВНA is a rectangle, then DK = AH = 45 mm. НК = ВС = 35 mm. Then AD = AН + DK + НK = 45 + 45 + 35 = 125 mm.

Determine the area of the trapezoid.

Savsd = (АD + ВС) * ОА / 2 = (125 + 35) * 60/2 = 4800 mm2.

Answer: The area of the trapezoid is 4800 mm2.