SOLUTION: In parallelogram ABCD, AB=125cm, AD=132cm, and the length of diagonal AC is 37cm. The area of the parallelogram, in cm squared, is a) 1155 b) 2310 c) 2442 d)4620 e)4884

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Question 1177486: In parallelogram ABCD, AB=125cm, AD=132cm, and the length of diagonal AC is 37cm. The area of the parallelogram, in cm squared, is
a) 1155 b) 2310 c) 2442 d)4620 e)4884
Found 3 solutions by ikleyn, MathLover1, greenestamps:
Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.

Using the Heron's formula for the triangle with the given sides, calculate its area.

It is 2310 square centimeters.

Then double this area, since the parallelogram is comprised of two such triangles.


The answer is option c).


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Solved.



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

AB=125cm, AD=132cm, and the length of diagonal AC is 37cm
are you sure this is right?
the length of diagonal AC is 37cm????????????? way to short for sides above, or the length of AB and AD is not correct

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Draw perpendicular AE from A to side CD.

Let CE=x so BE=132-x; let the length of AE be y.

Then right triangles AEC and AEB give us

x%5E2%2By%5E2+=+37%5E2 [1]
%28132-x%29%5E2%2By%5E2+=+125%5E2 [2]

Expand [2]:

132%5E2-264x%2Bx%5E2+=+125%5E2 [3]

Subtract [1] from [3]:

132%5E2-264x+=+125%5E2-37%5E2

Use a calculator and basic algebra to find x; then use [1] to find y.

Then the area of the parallelogram is base times height, which is 132 times y.

One of the given answer choices is correct....