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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #651 : Plane Geometry

Know that in a Major League Baseball infield the distance between home plate and first base is 90 feet and the infield is a perfect square.

If somebody wanted to know which had a larger area, a basketball court or a baseball infield, and they knew that a National Basketball Association court has a length of 94 feet and a width of 50 feet, what would they learn has a greater area?

Possible Answers:

The infield has a greater area.

The basketball court has a greater area.

They have the exact same area.

Correct answer:

The infield has a greater area.

Explanation:

The baseball infield is bigger than the basketball court in terms of area. The infield is 90x90=8100 square feet while the basketball court is 94x50=5076 square feet. Because 8100 square feet is greater than 5076 feet, the infield is bigger.

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Example Question #243 : Rectangles

A rectangular lot space at South Peninsula Trailer Park has a width of $20\;m$ (meters) and a length that is $3\;m$ more than twice the width of the lot space. What is the total area of the lot?

Possible Answers:

$860\;m^2$

$800\;m^2$

$740\;m^2$

$920\;m^2$

$975\;m^2$

Correct answer:

$860\;m^2$

Explanation:

To find the area, we need to know the length of the lot space. With the given information, we can solve for length by drafting an algebraic equation:

$\\length=2(width)+3\;m\\length=2(20\;m)+3\;m\\length=43\;m$

Now that we know the length, we can proceed to calculating the area:

$area=43\;m\cdot20\;m=860\;m^2$

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Example Question #94 : How To Find The Area Of A Rectangle

The shorter side of a rectangle is 8cm, the longer side is 15cm. What is the perimeter and the area of the rectangle?

Possible Answers:

$\textup{Perimeter=46; Area=120}$

$\textup{Perimeter=120; Area=46 }$

$\textup{Perimeter=46; Area=23}$

$\textup{Perimeter=23; Area=120 }$

Not enough information is given.

Correct answer:

$\textup{Perimeter=46; Area=120}$

Explanation:

To calculate the perimeter, recall that the perimeter is the sum off all the sides:

8+8+15+15=46

To calculate the area of a rectangle use the formula,

$A=l\cdot w$

In this particular case,

$\\l=15 \\w=8$

thus, area is

L*W=8*15=120

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Example Question #652 : Plane Geometry

Ricky wants to add an addition to his house. He needs to know how much flooring to get to cover the new addition. The new addition is 15 feet by 18 feet, and is in the shape of a rectangle. How much carpet should he get?

Possible Answers:

$150\ ft^2$

None of the answers given are correct

$270\ ft^2$

$500\ ft^2$

$300\ ft^2$

Correct answer:

$270\ ft^2$

Explanation:

Ricky's new addition has a length of 15 feet, and a width of 18 feet. To find the amount of carpet to get, (or just finding the area of the floor), just multiply 15 feet by 18 feet.

$15\cdot18=270$

Ricky needs 270 square feet of carpet

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Example Question #653 : Plane Geometry

The length of the long side of a rectangle is 14. The short side is half the length of the long side. What is the area of the rectangle?

Possible Answers:

$196\ inches^2$

$200\ inches^2$

$98\ inches^2$

$49\ inches^2$

$169\ inches^2$

Correct answer:

$98\ inches^2$

Explanation:

The area of any rectangle is

$length\cdot width$ .

One side is 14, and the other side is half of the given side. Half of 14 is 7, so now we have our length and width.

$7\cdot14=98$ inches^2

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Example Question #653 : Plane Geometry

Find the area of a rectangle with l=12 and w=10 .

Possible Answers:

A=44

A=30

A=60

A=120

Correct answer:

A=120

Explanation:

The formula for area is

A=l*w .

Plugging in the numbers,

A=12*10=120 .

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Example Question #102 : How To Find The Area Of A Rectangle

If the length of a rectangle is 40 feet and the width is 22 feet what is the area?

Possible Answers:

$124ft^{2}$

$880ft^{2}$

880ft

$808ft^{2}$

124 ft

Correct answer:

$880ft^{2}$

Explanation:

First we need to know that the formula for area of a rectangle is length times width. So since we know both length and width we can plug them into our equation

$40ft \cdot22ft=Area$ .

40 times 22 equals 880 and since we are multiplying two sides, both measured in feet, our answer is in square feet.

Our final answer is $880ft^{2}$

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Example Question #1 : How To Find The Length Of The Diagonal Of A Square

Side in the square below has a length of 12. What is the length of the diagonal ?

Square_diagonal

Possible Answers:

288

$12\sqrt{2}$

Cannot be determined from information given.

Correct answer:

$12\sqrt{2}$

Explanation:

Diagonal forms a triangle with adjacent sides . Since this is a square we know this is a right triangle and we can use the Pythagorean Theorem to determine the length of . Sides of length form each of the legs and is the hypotenuse. So the equation looks like this:

$12^{2}+12^{2}=d^{2}$

Solve for

$144+144=d^{2}$

$288=d^{2}$

$d=\sqrt{288}$

We can simplify this to

$\sqrt{144\cdot 2}=\sqrt{144}\cdot \sqrt{2}=12\sqrt{2}$

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Example Question #2 : How To Find The Length Of The Diagonal Of A Square

A man wants to build a not-quite-regulation softball field on his property and finds that he only has enough room to make the distance between home plate and first base 44 feet. How far (nearest foot) will it be from home plate to second base, assuming he builds it to that specification?

(Note: the four bases are the vertices of a perfect square, with the bases called home plate, first base, second base, third base, in that order).

Possible Answers:

$62\; \textrm{ft}$

$88\; \textrm{ft}$

$66\; \textrm{ft}$

$72\; \textrm{ft}$

$76\; \textrm{ft}$

Correct answer:

$62\; \textrm{ft}$

Explanation:

The path from home plate to first base is a side of a perfect square; the path from home plate to second base is a diagonal. As two sides and a diagonal form a $45^{\circ } -45^{\circ } -90^{\circ }$ triangle, the diagonal measures $\sqrt{2}$ as long as a side.

The distance to second base from home is $\sqrt{2}$ times the distance to first base:

$d = 44 \cdot \sqrt{2} \approx 44 \cdot 1.414 \approx 62$

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Example Question #1 : How To Find The Length Of The Diagonal Of A Square

A square lot has an area of 1,200 square meters. To the nearest meter, how far is it from one corner to the opposite corner?

Possible Answers:

$196\ meters$

$25\ meters$

$300\ meters$

$98\ meters$

$49\ meters$

Correct answer:

$49\ meters$

Explanation:

A square is also a rhombus, so its area can be calculated as one half the product of its diagonals:

$A= \frac{1 }{2}d^{2}$ ,

where is the common diagonal length.

Since A=1200 , $1200 = \frac{1 }{2}d^{2}$ .

$2400 = d^{2}$

$d = \sqrt{2400} \approx 49$

The distance between opposite corners is about 49 meters.

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #651 : Plane Geometry

Example Question #243 : Rectangles

Example Question #94 : How To Find The Area Of A Rectangle

Example Question #652 : Plane Geometry

Example Question #653 : Plane Geometry

Example Question #653 : Plane Geometry

Example Question #102 : How To Find The Area Of A Rectangle

Example Question #1 : How To Find The Length Of The Diagonal Of A Square

Example Question #2 : How To Find The Length Of The Diagonal Of A Square

Example Question #1 : How To Find The Length Of The Diagonal Of A Square

All Basic Geometry Resources

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