Question

The Moore family’s backyard is shaped like a trapezoid as shown. The area of the backyard is 8,580 square feet. What is the perimeter of the yard? Explain how you found your answer.

Answer 1

See Explanation

Explanation:

Your question do not have enough details for it to be answered. I will solve your question on a general terms using the attached image of a trapezoid

Given

`Area = 8580ft^2`

From the attachment, we have:

`BC = 100ft`

`AD = 80ft`

`h = 60ft` --- height

The perimeter (P) of a trapezoid is:

`P = AB + BC + CD + AD`

Substitute values for AD, BC

`P = AB + 100 + CD + 80`

Collect Like Terms

`P = AB + CD + 80+ 100`

`P = AB + CD + 180`

Next, is to calculate the lengths of AB and CD or the sum: AB + CD

The area of a trapezoid is:

`Area = (1)/(2)(AB + CD) * h`

Substitute values for Area and h

`8580= (1)/(2)(AB + CD) * 60`

Multiply both sides by 2

`2*8580= (1)/(2)(AB + CD) * 60*2`

`17160= (AB + CD) * 60`

Divide both sides by 60

`(17160)/(60)= ((AB + CD) * 60)/(60)`

`286 = AB + CD`

`AB + CD=286`

Substitute 286 for AB + CD in:
`P = AB + CD + 180`

`P = 286 + 180`

`P = 466`

The perimeter of the backyard is 466ft.

The above steps should give you a hint on how to solve your actual question.