You are putting in a lawn in your backyard. Your backyard is shaped like a trpezoid(as shown on attachment) You need to put down 3 inches of soil.(Notice that the top of the soil will be congruent and parallel to the bottom of the soil) How many cubic YARDS of soil will you have to order?
Help would be awesome!!<3

- anonymous

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- anonymous

##### 1 Attachment

- anonymous

do you know how to find out the area of the trapezoid?

- anonymous

Isn't it 21+33
-------*h?
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- anonymous

okay. so what is the area in your question?

- anonymous

well the answer to the equation I typed is 540ft^2

- anonymous

okay. yes, the area of the trapezoid is 540 square feet.
if you are to cover 540 square feet in 3 inches of soild, how much would the volume of the soil be?
remember, volume = area times height.

- anonymous

but isn't the area in feet and the soil in inches? so how would I convert that if I have too?

- anonymous

1 foot is 12 inches. so recalculate the area in terms of inches.

- anonymous

and tht would be multipling the area by 12 right? and I got the volume of the solid would be 19,440inches

- anonymous

no, you have to multiply the area by 144. because area is in SQUARE feet.
a square of 1 foot by 1 foot is 1 X 1 square feet in area = 1 square feet in area.
if you replece 1 foot by 12 inches, the square's area is
12 inches X 12 inches = 144 square inches.

- anonymous

oh okay so I got 77,760 inches. Would this be the area of the soil I'm putting down or the trapezoid and the soil?

- anonymous

area is not in inches. area is in square inches.
so, the area of the lawn is 77760 square inches.
so what is the volume of the layer of soil of height 3 inches spread out on that area?

- anonymous

How would you find that?

- anonymous

volume = area*height.

- anonymous

So 77760 in^2 *20=1,555,200inches^2 what do I do next?

- anonymous

why are you multiplying it by 20? I thought the soil was 3 inches height above the ground?

- anonymous

ohh okay sorry I must have spaced out there yeah it's 3 inches so I got 233,280 what do I do next?

- anonymous

what does the number 233,280 represent?

- anonymous

The area of the trapezoid with the soil on top right?

- anonymous

nope. remember what you were trying to calculate? remember why you multiplied the area of the trapezoid with the height of the soil?

- anonymous

no i don't really remember why.....sorry but this is new to me.

- anonymous

come on man! we were trying to calculate the volume of the soil! just scroll up and see. so, tell me what does the number 233,280 represent?

- anonymous

The volume of the soil?:)

- anonymous

yes. but in what measurement? is it cubic feet? or cubic yards? or leaves in the trees in your garden, or number of rats in new york?
just giving a number doesn't tell me anything. you have to say what the number's significance is.

- anonymous

inches^2, haha

- anonymous

try again. you multiplied area, interms of inches^2, times height, in terms if inches.
if you multiply inches^2 by inches, would you get inches^2 or inches^3?

- anonymous

inches^3

- anonymous

okay, so the volume of the amount of soil you would have to order is 233,280 inches^3

- anonymous

how much is that in cubic yards? remember, one yard is 3 feet. and 1 feet is 12 inches.

- anonymous

Okay so I would multiple byt 12 then by 3?

- anonymous

that is converting 1 yard to 1 inch.

- anonymous

sorry, i meant. one yard = 36 inches.

- anonymous

so divide by 36?

- anonymous

nope.
1 cubic yard is 1 yard by 1 yard by 1 yard.
which means 1 cubic yard is 36 inches by 36 inches by 36 inches.

- anonymous

So divide by 36 three times?

- anonymous

oh yeah okay I got it thanks SOOOOOOOOOOOO much!!<333

- anonymous

you are welcome.

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