It is known that the area of a right triangle is 12cm2 and the perimeter is 122cm, then the radius of the circumscribed circle of the right triangle is___ cm．

It is known that the area of a right triangle is 12cm2 and the perimeter is 122cm, then the radius of the circumscribed circle of the right triangle is___ cm．

If the right side of the right triangle is a, B, and the hypotenuse is C, then from the meaning of the title: s △ = 12ab = 12, a + B + C = 122, a + B = 24, a + B = 122-c, according to the Pythagorean theorem, A2 + B2 = C2, (a + b) 2-2ab = C2, (122-c) 2-48 = C2, the solution is C = 52, so the radius is 522cm

A trapezoid, if the top and bottom increase by 3 cm, becomes a square; if the top and bottom decrease by 3 cm, becomes a triangle. The area of this trapezoid is () square cm

Because the upper bottom is reduced by 3cm, it becomes a triangle, so the upper bottom = 3cm
Because the upper bottom is increased by 3 cm, it becomes a square, so the lower bottom is 6 cm
And height = bottom = 6cm
So area = (upper bottom + lower bottom) * height / 2 = (3 + 6) * 6 / 2 = 27

The height of a trapezoid is 10 cm. If its top and bottom are reduced by 6 cm, it becomes a triangle. If it is increased by 4 cm, it becomes a square. Find the area of the trapezoid

If the upper bottom is reduced by 6cm, it becomes a triangle, indicating that the upper bottom of trapezoid L1 = 6
If the upper bottom is increased by 4cm, it becomes a square, indicating that the lower bottom of trapezoid L2 = 10
The height of trapezoid is h = 10cm
According to the trapezoidal area formula
S=(1/2)*(L1+L2)*H=80(cm^2)