Question

The area of trapezoids ABEC, ABFD, and $ABFC are 133, 140, and 161 square feet, respectively. Quadrilateral ABED is a rectangle. The length of segment DE is 8 feet. What is the length of segment CF

Answer 1

The length of segment CF is 15

Explanation:

Let
`A_(1)` = ABEC = 133

Let
`A_(2)` = ABFD = 140

Let A = ABFC = 161

Let
`A_(rectangle)` = A = 8 AD

Let x = CF

`A_(1)`+
`A_(2)` = A +
`A_(0)`

133 + 140 = 161 +
`A_(0)`

`A_(0)` = 133 + 140 - 161

`A_(0)` = 122
`A_(0)` = 8AD

8AD = 122

AD=
`(122)/(8)`

AD=14

A=
`((8+x))/(2)` × AD

161 =
`((8+x))/(2)` ×14

161 = (8 + x )×7

23 = 8 + x

x = 23 - 8

x= 15