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SSAT Middle Level Math : How to find a rectangle on a coordinate plane

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Example Questions

Example Question #1 : How To Find A Rectangle On A Coordinate Plane

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In the above figure Dr. Robinson's shed is represented by the red square, and the shed has a perimeter of $\small 12$ $\displaystyle \small 12$ yards. Find how much area Dr. Robinson has in his backyard--excluding the area that the shed occupies.

Possible Answers:

$\small 110$ $\displaystyle \small 110$ $\small yards^2$ $\displaystyle \small yards^2$

$\small 120$ $\displaystyle \small 120$ $\small yards^2$ $\displaystyle \small yards^2$

$\small 129$ $\displaystyle \small 129$ $\small yards^2$ $\displaystyle \small yards^2$

$\small \small 111$ $\displaystyle \small \small 111$ $\small yards^2$ $\displaystyle \small yards^2$

Correct answer:

$\small \small 111$ $\displaystyle \small \small 111$ $\small yards^2$ $\displaystyle \small yards^2$

Explanation:

To find how much area Dr. Robinson has around his shed in his backyard, first apply the formula: $\small \small P=4S$ $\displaystyle \small \small P=4S$ , where $\small S$ $\displaystyle \small S$ represents one side of the red shed. Given that $\small \small P=12$ $\displaystyle \small \small P=12$
$\small S$ $\displaystyle \small S$ must equal $\small 3$ $\displaystyle \small 3$ because $\small 4\times3=12$ $\displaystyle \small 4\times3=12$ .

Now you have enough information to find the area of the red shed.
Apply the formula: $\small A=S^2$ $\displaystyle \small A=S^2$
$\small A=3^2=3\times3=9$ $\displaystyle \small A=3^2=3\times3=9$

Since the rectangular fence has a width of $\small 15$ $\displaystyle \small 15$ yards and a length of $\small 8$ $\displaystyle \small 8$ yards, apply the formula: $\small Area=width\times length$ $\displaystyle \small Area=width\times length$ in order to find the area of the entire backyard.
Thus,
$\small Area=15\times8=120$ $\displaystyle \small Area=15\times8=120$

Then simply find the difference between the area of the entire yard and the area of the shed.

Thus the final solution is:
$\small 120-9=111$ $\displaystyle \small 120-9=111$

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Example Question #2 : How To Find A Rectangle On A Coordinate Plane

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Identify the correct set of coordinates for rectangle $\small ABCD$ $\displaystyle \small ABCD$ .

Possible Answers:

$\small (-11,3),(-11,7),(-3,-3),(3,7)$ $\displaystyle \small (-11,3),(-11,7),(-3,-3),(3,7)$

$\small (-11,3),(11,7),(3,3),(-3,7)$ $\displaystyle \small (-11,3),(11,7),(3,3),(-3,7)$

$\small (-11,3),(-11,7),(3,3),(3,7)$ $\displaystyle \small (-11,3),(-11,7),(3,3),(3,7)$

$\small (11,3),(-10,7),(3,3),(3,7)$ $\displaystyle \small (11,3),(-10,7),(3,3),(3,7)$

Correct answer:

$\small (-11,3),(-11,7),(3,3),(3,7)$ $\displaystyle \small (-11,3),(-11,7),(3,3),(3,7)$

Explanation:

To identify the correct set of coordinate points for rectangle $\small ABCD$ $\displaystyle \small ABCD$ , note that the correct set must have two sets of matching $\small x$ $\displaystyle \small x$ coordinates and two sets of matching $\small y$ $\displaystyle \small y$ coordinates. The only answer choice that meets these specifications is: $\small \small (-11,3),(-11,7),(3,3),(3,7)$ $\displaystyle \small \small (-11,3),(-11,7),(3,3),(3,7)$

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Example Question #223 : Ssat Middle Level Quantitative (Math)

Dr. Robinson recently put a rectangular fence around his backyard. The fence has a width of $\small 15$ $\displaystyle \small 15$ yards and a length of $\small 8$ $\displaystyle \small 8$ yards. If Dr. Robinson paid $\small \small \$ 12.50$ $\displaystyle \small \small \$ 12.50$ for every yard of fence, how much did the fence cost?

Possible Answers:

$\small \$525$ $\displaystyle \small \$525$

$\small \$575$ $\displaystyle \small \$575$

$\small \$625$ $\displaystyle \small \$625$

$\small \$375$ $\displaystyle \small \$375$

Correct answer:

$\small \$575$ $\displaystyle \small \$575$

Explanation:

To find the cost of the fence, apply the formula $\small P=2(width)+2(length)$ $\displaystyle \small P=2(width)+2(length)$ in order to first find the length of the perimeter of the fence.

Then multiply the perimeter by $\small \$12.50$ $\displaystyle \small \$12.50$ .

Thus, the solution is:

$\small P=2(15)+2(8)$ $\displaystyle \small P=2(15)+2(8)$
$\small P=30+16$ $\displaystyle \small P=30+16$
$\small P=46$ $\displaystyle \small P=46$

$\small 46\times12.5=575$ $\displaystyle \small 46\times12.5=575$

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Example Question #224 : Ssat Middle Level Quantitative (Math)

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The rectangle shown above has a width of $\small 14$ $\displaystyle \small 14$ and a length of $\small 4$ $\displaystyle \small 4$ . Find the area and perimeter of the rectangle.

Possible Answers:

$\small \small A=56 units^2, P=36$ $\displaystyle \small \small A=56 units^2, P=36$

$\small \small A=50 units^2, P=34$ $\displaystyle \small \small A=50 units^2, P=34$

$\small \small A=43 units^2, P=26$ $\displaystyle \small \small A=43 units^2, P=26$

$\small \small A=36 units^2, P=36$ $\displaystyle \small \small A=36 units^2, P=36$

Correct answer:

$\small \small A=56 units^2, P=36$ $\displaystyle \small \small A=56 units^2, P=36$

Explanation:

To solve this problem apply the formulas: $\small Area=width\times length$ $\displaystyle \small Area=width\times length$ & $\small Perimeter=2(w)+2(l)$ $\displaystyle \small Perimeter=2(w)+2(l)$

Thus, the solution is:

$\small A=14\times4=56$ $\displaystyle \small A=14\times4=56$
$\small P=2(14)+2(4)=28+8=36$ $\displaystyle \small P=2(14)+2(4)=28+8=36$

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SSAT Middle Level Math : How to find a rectangle on a coordinate plane

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #1 : How To Find A Rectangle On A Coordinate Plane

Example Question #2 : How To Find A Rectangle On A Coordinate Plane

Example Question #223 : Ssat Middle Level Quantitative (Math)

Example Question #224 : Ssat Middle Level Quantitative (Math)

All SSAT Middle Level Math Resources

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