Answer:
length of segment YZ is 8 cm
Step-by-step explanation:
given data
AB = 16 cm
DA = 3 cm
AB and DA form interior angle = 45-degre
WX ≠ YZ
WX = 16 cm
to find out
length of segment YZ
solution
area of △ABD is the same as the area of △BCD
and
area of △ABD is express as
area of △ABD = AB × AD × sin(45) ÷ 2 ............1
put here value
area of △ABD = 16 × 3√2 × sin(45) ÷ 2
area of △ABD = 24
and
area of the parallelogram is
area of the parallelogram = 24 × 2
area of the parallelogram = 48
so
now we will consider here YZ = x
and Since ZY XW is isosceles trapezoid
so here we can say that
WM = ZM = (16 - x) ÷ 2 .......................2
so area of trapezoid will be
area of trapezoid = .......................3
area of trapezoid =
48 =
solve it we get
x = 8
so length of segment YZ is 8 cm
