ABC is a right triangle with each leg divided into 5 equal segments as shown. If the largest trapezoid has the area 36 cm^2, then the area of the second smallest trapezoid is what?
2 answers
"as shown" ???
if the legs are 5x and 5y, then
the area of the smallest trapezoid is 1/2 xy
the 2nd smallest is 1/2 * 4xy - 1/2 xy = 1/2 * 3xy
the largest is 1/2 * 25xy - 1/2 * 16xy = 1/2 * 9xy
1/2 * 9xy = 36
xy = 8
so the 2nd smallest is 1/2 * 24 = 12
the area of the smallest trapezoid is 1/2 xy
the 2nd smallest is 1/2 * 4xy - 1/2 xy = 1/2 * 3xy
the largest is 1/2 * 25xy - 1/2 * 16xy = 1/2 * 9xy
1/2 * 9xy = 36
xy = 8
so the 2nd smallest is 1/2 * 24 = 12
5 answers