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Basic Geometry : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

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9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #35 : How To Find The Length Of The Diagonal Of A Rectangle

A rectangle has sides of length 3cm and 9cm . What is the length of its diagonal?

Possible Answers:

90 cm

$3\sqrt{5}cm$

$3\sqrt{10} cm$

$\sqrt{30}cm$

10cm

Correct answer:

$3\sqrt{10} cm$

Explanation:

The diagonal of a rectangle forms the hypotenuse of a right triangle with one long and one short side of the rectangle. Therefore, to find the diagonal, we use the Pythagorean Theorem using the two side lengths and solving for the hypotenuse:

a^2+b^2=c^2

3^2+9^2=c^2

9+81=c^2

90=c^2

$\sqrt{90}=\sqrt{c^2}$

$c=\sqrt{90}$

Then, all we have to do is simplify the radical, as follows:

$\sqrt{90}=\sqrt{9*10}$

$\sqrt{9*10}=\sqrt{9}*\sqrt{10}$

$\sqrt{9}*\sqrt{10}=3*\sqrt{10}=3\sqrt{10}$

Therefore, $c=3\sqrt{10}$ .

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Example Question #34 : How To Find The Length Of The Diagonal Of A Rectangle

A rectangular pen has side lengths of 15 meters and 10 meters. Suppose a fence must be built from one corner diagonally across to the opposite corner. Approximately how many meters of fence will be needed?

Possible Answers:

35m

12m

None of these.

20m

18m

Correct answer:

18m

Explanation:

Rectangles have long and short sides which are opposite each other. The diagonal that runs from the opposite corner across the rectangle forms a right angle.

Use Pythagorean Theorem to find the length of the diagonal.

a^2+b^2=c^2

10^2+15^2=c^2

$\sqrt{c^2}=\sqrt{325}=\mathbf{18}$ (approximately)

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Example Question #551 : Plane Geometry

If a laptop screen has a length of $20\;cm$ and an area of $240\;cm^2$ , what is the diagonal length of the rectangle? Round to the nearest tenth.

Possible Answers:

$30.1\;cm$

$21.1\;cm$

$23.3\;cm$

$22.7\;cm$

$26.2\;cm$

Correct answer:

$23.3\;cm$

Explanation:

To find the diagonal length, we must first find the width of the rectangular screen. With the given information, we can use the formula for area of a rectangle to find the missing value:

$\\area=length\cdot width\\ \\240\;cm^2=20\;cm\cdot width\\ \\width=\frac{240\;cm^2}{20\;cm}=12\;cm$

Now that we know the length and width, we can use the Pythagorean Theorem to solve for the diagonal length:

$\\c^2=20\;cm^2+12\;cm^2\\c^2=400\;cm^2+144\;cm^2\\c^2=544\;cm^2\\c=\sqrt544\;cm^2=23.32\;cm\approx23.3\;cm$

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Example Question #37 : How To Find The Length Of The Diagonal Of A Rectangle

The length of a rectangle is 4cm and the width is 3cm. What is the length of the diagonal?

Possible Answers:

$7\ cm$

$12\ cm$

$1\ cm$

$5\ cm$

$25\ cm$

Correct answer:

$5\ cm$

Explanation:

The diagonal can be found using Pythagorean Theorem.

length^2+width^2=diagonal^2

(4)^2+(3)^2=x^2

25=x^2

x=5

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Example Question #1 : How To Find The Area Of A Rectangle

A rectangle has a perimeter of $40\; m$ . The length is ten meters more than the width. What is the area of the rectangle?

Possible Answers:

$80\; m^{2}$

$75\; m^{2}$

$60\; m^{2}$

$120\; m^{2}$

$150\; m^{2}$

Correct answer:

$75\; m^{2}$

Explanation:

Given a rectangle, the general equation for the perimeter is P = 2l + 2w and area is A = lw where is the length and is the width.

Let = width and x + 10 = length

So the equation to solve becomes 40 = 2x + 2(x+10) so x = 5 thus the width is $5\; m$ and the length is $15\; m$ .

Thus the area is $5\cdot 15= 75 \; m^{2}$

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Example Question #1 : How To Find The Area Of A Rectangle

Which of the following information would not be sufficient to find the area of a rectangle?

Possible Answers:

The perimeter and the length of one side.

The lengths of one side and a diagonal.

The lengths of one pair of opposite sides.

All of the other choices list information that would be sufficient.

The lengths of one pair of adjacent sides.

Correct answer:

The lengths of one pair of opposite sides.

Explanation:

The area of a rectangle can be calculated by multiplying the lengths of two adjacent sides. All of the choices given lists sufficient information, with one exception. We examine each of the choices.

The lengths of one pair of adjacent sides: This choice is false, as is directly stated above.

The perimeter and the length of one side: Using the perimeter formula, you can find the length of an adjacent side, making this choice false.

The lengths of one side and a diagonal: using the Pythagorean Theorem, you can find the length of an adjacent side, making this choice false.

The lengths of one pair of opposite sides: this gives you no way of knowing the lengths of the adjacent sides. This is the correct choice.

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Example Question #3 : How To Find The Area Of A Rectangle

Find the area of the polygon.

Possible Answers:

180

175

200

165

160

Correct answer:

180

Explanation:

Drawing a vertical line at the end of the side of length divides the shape into a rectangle and a right triangle.

The sum of the areas of the two shapes is the area of the polygon. Multiply the length of the rectangle by its width to find the area of the rectangle, and use the formula $A = \frac{1}{2}bh$ , where is the base and is the height of the triangle, to find the area of the triangle. Adding them together gives the answer.

$A_{total}=A_{rec}+A_{tri}$

$A_{total}=(8*20)+\frac{1}{2}(5*8)$

A = 180

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Example Question #1 : How To Find The Area Of A Rectangle

One side of a rectangle is 7 inches and another is 9 inches. What is the area of the rectangle in inches?

Possible Answers:

Correct answer:

Explanation:

To find the area of a rectangle, multiply its width by its height. If we know two sides of the rectangle that are different lengths, then we have both the height and the width.

$9\cdot 7=63$

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Example Question #2 : How To Find The Area Of A Rectangle

What is the area of the rectangle in the diagram?

Possible Answers:

$19\ cm^{2}$

$90\ cm^{2}$

$49\ cm^{2}$

$144\ cm^{2}$

$84\ cm^{2}$

Correct answer:

$84\ cm^{2}$

Explanation:

The area of a rectangle is found by multiplying the length by the width.

Area=l(w)

The length is 12 cm and the width is 7 cm.

$12\cdot 7=84$

Therefore the area is 84 cm².

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Example Question #2 : How To Find The Area Of A Rectangle

What is the area of a rectangle whose length and width is inches and inches, respectively?

Possible Answers:

$148\, in^2$

$64\, in^2$

$252\,in^2$

$220\, in^2$

$128\, in^2$

Correct answer:

$252\,in^2$

Explanation:

The area of any rectangle with length, and width, is:

$A=l\times w$

$A=14\times 18$

$A=252\, in^2$

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All Basic Geometry Resources

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Basic Geometry : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #35 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #34 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #551 : Plane Geometry

Example Question #37 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #1 : How To Find The Area Of A Rectangle

Example Question #1 : How To Find The Area Of A Rectangle

Example Question #3 : How To Find The Area Of A Rectangle

Example Question #1 : How To Find The Area Of A Rectangle

Example Question #2 : How To Find The Area Of A Rectangle

Example Question #2 : How To Find The Area Of A Rectangle

All Basic Geometry Resources

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