ISEE Lower Level Quantitative Reasoning - How to find a parallelogram on a coordinate plane

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Given that the above parallelogram has base sides with a length of and diagonal sides with a length of $\sqrt{10}$ what is the perimeter of the parallelogram?

$P=2(\sqrt{10}+4)$

$P=(\sqrt{10}+4)$

$P=2(\sqrt{10}+3)$

$P=2(\sqrt{10}-4)$

Explanation

In order to find the perimeter of the parallelogram apply the formula: , where the length of one diagonal side and the length of one base.

In this problem, $a=\sqrt{10}$ and .
Thus, the correct answer is: $P=2(\sqrt{10}+4)$

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The parallelogram shown above has a height of and a base of length . Find the perimeter of the parallelogram.

$P=2(\sqrt{20}+5)$

$P=2(\sqrt{20}+4)$

$P=(\sqrt{20}+5)$

Explanation

In order to find the correct perimeter of the parallelogram apply the formula: , where the length of one of the diagonal sides and the length of the base.

In order to find the length of side , apply the formula: . By drawing an altitude from point to , a right triangle is formed with a base that has a length of and a height of .

Thus, the solution is:

length of side

$a=\sqrt{20}$

Therefore,

$P=2(\sqrt{20}+b)$

$P=2(\sqrt{20}+5)$

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What is the area of the parallelogram shown above?

square units

Explanation

To find the area of the parallelogram that is shown, apply the formula: $A=base\times height$
Since the parallelogram has a base of and a height of the solution is:
$A=4\times 3=12$