SOLUTION: Rose’s garden is in the shape of a trapezoid. If the height of the trapezoid is 16 m, one base is 20 m, and the area is 224 m2, find the length of the other base.

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Question 62696: Rose’s garden is in the shape of a trapezoid. If the height of the trapezoid
is 16 m, one base is 20 m, and the area is 224 m2, find the length of the other base.
Found 2 solutions by checkley71, joyofmath:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
AREA=(S1+S2)/2*16
224=[(20+S2)/2]*16
224=[20+S2)*8
224=160+8*S2
224-160=8*S2
8*S2=64
S2=64/8
S2=8m THE LENGTH OF THE SECOND SIDE.
PROOF
224=[(20+8)2]*16
224=[(28/2]*16
224=14*16
224=224



Answer by joyofmath(189) About Me  (Show Source):
You can put this solution on YOUR website!
Rose’s garden is in the shape of a trapezoid. If the height of the trapezoid
is 16 m, one base is 20 m, and the area is 224 m2, find the length of the other base.
The formula for the area of a trapezoid is: a=%281%2F2%29h%28B%5B1%5D%2BB%5B2%5D%29 where B%5B1%5D is one base and B%5B2%5D is the other base.
We know that h=16, B%5B1%5D=20, and a=224.
So, plug these numbers into the area formula and 224=%281%2F2%29%2816%29%2820%2BB%5B2%5D%29.
Or, 224=8%2820%2BB%5B2%5D%29.
So, 224=160%2B8B%5B2%5D or 64=8B%5B2%5D. So, B%5B2%5D+=+8.
Let's verify that B%5B2%5D+=+8.
a=%281%2F2%29h%28B%5B1%5D%2BB%5B2%5D%29+=%281%2F2%29%2816%29%2820%2B8%29=8%2828%29=224.