how much of the base of the rectangle needs to be removed so that the two shapes will have the same area

Question

A trapzoid and a rectangle have the same height. the larger base of the trapezoid is the same length as the base of the rectangle and twice the length of the smaller base of the trapzoid.how much of the base of the rectangle needs to be removedso that the two shapes will have the same area?

Answer 1

rektangel area=leng*hi

trapazoid area=hi*(leng+0.5leng)/2=(1.5/2)leng*hi...=0.75 lend*hi

kut rektangel leng bi 25%

Answer 2

Area of rectangle is ah, where h is the common height of the rectangle and trapezoid, and a is the common length of the larger base of the trapezoid and the rectangle. The smaller base of the trapezoid is a/2. The area of the trapezoid is ah/2 (the area of the rectangle made up of the trapezoid's shorter base and its height, h)+the areas of the triangular "wings". If we call the bases of the triangles x and y, we know that x+y=a/2 because the longer base of the trapezoid is a/2. The height of both triangular wings is h and their total area is xh/2+yh/2=h(x+y)/2=ah/4. So the total area of the trapezoid=ah/2+ah/4=3ah/4. If the rectangle keeps the same height h but changes its base length, b, to make the areas the same, then hb=3ah/4, so b=3a/4 compared to a, which it was before. So the reduction is a/4 or 25%.