Find the length y in the figure The area of the shaded regio

Find the length y in the figure. The area of the shaded region is given. (Round your answer to two decimal places.) and  Find the length y in the figure. The area of the shaded region is given.

Solution

a) base of triangle = y , height of triangle = y

area of triangle =(1/2)*base *height

area of triangle =(1/2)*y*y

area of triangle =(1/2)y²

base of rectangle = y , height of rectangle  = y

area of rectangle  =base *height

area of rectangle  =y*y

area of rectangle  =y²

total area of figure =(1/2)y² +y² =146

(3/2)y² =146

y² =146*2/3

y =9.87 in

b)

base of triangle = y , height of triangle = y

area of triangle =(1/2)*base *height

area of triangle =(1/2)*y*y

area of triangle =(1/2)y²

base of rectangle = 1cm , height of rectangle  = y

area of rectangle  =base *height

area of rectangle  =1*y

area of rectangle  =y

total area of figure =(1/2)y² +y =1200

y² +2y=2400

y² +2y-2400=0

y=[-2+(2²-4*1*(-2400))]/2

y=48cm