What is the missing length !10 POINTS!

z = 16.4 ft

Step-by-step explanation:

The figure has a shape of a TRAPEZIUM.

The AREA of a TRAPEZIUM is expressed as:

Area (A) = 1/2 (a + b) h

Where "a" and "b" are the lengths of the trapezium.

h is the hight.

From the question:

Area (A) = 135 ft^2

Height (h) = 10 ft

a = Length = 10.6ft

b = (the other length) = z

LET'S substitute values into :

Area (A) = 1/2 (a + b) h

135 ft^2 = 1/2 ( 10.6ft + z) 10 ft

Let's simplify and solve for z

135 = 5 (10. 6 + z)

135 = 53 + 5z

Let's collect like terms and solve for z

5z = 135 - 53

5z = 82

Divide through by 5

z = 82 / 5

z = 16.4 ft

Math is fun, let's keep learning

z = 16.4 feet

Step-by-step explanation:

The formula for determining the area of a trapezoid is expressed as

Area = 1/2(a + b)h

Where

a and b are the length of The bases are the 2 sides of the trapezoid which are parallel with one another.

h represents the height of the trapezoid.

From the information given,

a = 10.6 feet

b = z feet

h = 10 ft

Area = 135 ft.²

Therefore,

135 = 1/2(10.6 + z)10

Cross multiplying by 2, it becomes

135 × 2 = (10.6 + z)10

270 = (10.6 + z)10

Dividing both sides of the equation by 10, it becomes

27 = 10.6 + z

z = 27 - 10.6

z = 16.4 feet