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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #5 : Plane Geometry

Find the area of the shaded region:

Screen_shot_2014-03-01_at_9.02.03_pm

Possible Answers:

$6\pi - 18cm^2$

$6\pi - 9cm^2$

$9\pi - 18cm^2$

$9\pi - 9cm^2$

$9\pi - 24cm^2$

Correct answer:

$9\pi - 18cm^2$

Explanation:

To find the area of the shaded region, you need to subtract the area of the triangle from the area of the sector:

$A = A_{sector} - A_{triangle}$

$A = \pi r^2 (part) - \frac{1}{2} (b)(h)$

Where is the radius of the circle, part is the fraction of the circle, is the base of the triangle, and is the height of the triangle

Plugging in our values, we get

$A = \pi (6cm^2) (\frac{90}{360}) - \frac{1}{2} (6cm)(6cm)$

$A = 9\pi - 18cm^2$

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Example Question #7 : Plane Geometry

Find the area of the shaded region:

Screen_shot_2014-03-01_at_9.04.49_pm

Possible Answers:

$\frac{25\pi }{6}- \frac{25\sqrt{3}}{6} cm^2$

$\frac{25\pi }{6}- \frac{25\sqrt{3}}{4} cm^2$

$\frac{25\pi }{4}- \frac{25\sqrt{3}}{4} cm^2$

$\frac{25\pi }{4}- \frac{25\sqrt{3}}{6} cm^2$

$\frac{25\pi }{6}- \frac{25\sqrt{2}}{4} cm^2$

Correct answer:

$\frac{25\pi }{6}- \frac{25\sqrt{3}}{4} cm^2$

Explanation:

To find the area of the shaded region, you need to subtract the area of the equilateral triangle from the area of the sector:

$A = A_{sector} - A_{equilateral triangle}$

$A = \pi r^2 (part) - \frac{s^2 \sqrt{3}}{4}$

Where is the radius of the circle, part is the fraction of the circle, and is the side of the triangle

Plugging in our values, we get

$A = \pi (5cm^2) \frac{60}{360} - \frac{(5cm)^2\sqrt{3}}{4}$

$A=\frac{25\pi }{6}- \frac{25\sqrt{3}}{4} cm^2$

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

Find the area of the shaded region:

Possible Answers:

$30 \pi\ m^2$

$32 \pi\ m^2$

$24 \pi\ m^2$

$26 \pi\ m^2$

$28 \pi\ m^2$

Correct answer:

$28 \pi\ m^2$

Explanation:

The formula for the area of the shaded region is

$A = A_{large circle}-A_{small circle}= \pi r_{large}^2 - \pi r_{small}^2,$

where is the radius of the circle.

Plugging in our values, we get:

$A = \pi (8\ m)^2 - \pi (6\ m)^2$

$A = 28 \pi\ m^2$

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

Find the area of the following octagon:

Possible Answers:

$288\sqrt{2}+288\ m^2$

$200\sqrt{2}+288\ m^2$

$288\sqrt{2}+280\ m^2$

$280\sqrt{2}+288\ m^2$

$280\sqrt{2}+280\ m^2$

Correct answer:

$288\sqrt{2}+288\ m^2$

Explanation:

The formula for the area of a regular octagon is:

$A = \frac{1}{2}(perimeter)(apothem)$

Plugging in our values, we get:

$A = \frac{1}{2}(96\ m)(6\sqrt{2}\ m+6\ m)$

$A = 288\sqrt{2}+288\ m^2$

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

Find the area of a rectangle with a base of (x + 3) and a width of (x - 3) in terms of .

Possible Answers:

$x^{2 } - 3x - 9$

$x^{2 } + 9$

$x^{2}$

none of the other answers

$x^{2} - 9$

Correct answer:

$x^{2} - 9$

Explanation:

This problem simply becomes a matter of FOILing (first outer inner last)

The area of the shape is Base times Height.

So, multiplying (x + 3) and (x - 3) using FOIL, we get an area of $x^{2} - 9$

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Example Question #11 : Plane Geometry

Find the area of a square whose diagonal is .

Possible Answers:

144

none of these answers

Correct answer:

Explanation:

If the diagonal of a square is , we can use the pythagorean theorem to solve for the length of the sides.

= length of side of the square

Doing so, we get $2x^{2} = 144$

$x = \sqrt{72}$

To find the area of the square, we square , resulting in .

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Example Question #1 : How To Find An Angle In A Polygon

What is the magnitude of the interior angle of a regular nonagon?

Possible Answers:

129^o

144^o

140^o

135^o

Correct answer:

140^o

Explanation:

The equation to calculate the magnitude of an interior angle is $\frac{180(n-2)}{n}=int\ angle$ , where is equal to the number of sides.

For our question, n=9 .

$int\ angle= \frac{180(9-2)}{9}=\frac{(180)(7)}{9}=140^o$

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Example Question #12 : Geometry

What is the interior angle measure of any regular heptagon?

Possible Answers:

125.8

135

130.2

128.6

Correct answer:

128.6

Explanation:

To find the angle of any regular polygon you find the number of sides, . In this example, n=7 .

You then subtract 2 from the number of sides yielding 5.

Take 5 and multiply it by 180 degrees to yield the total number of degrees in the regular heptagon. 5*180=900

Then to find one individual angle we divide 900 by the total number of angles, 7.

$\frac{900}{7}=128.6$

The answer is 128.6 .

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Example Question #13 : Other Polygons

A regular polygon with sides has exterior angles that measure $1.5^{\circ }$ each. How many sides does the polygon have?

Possible Answers:

120

180

This figure cannot exist.

240

150

Correct answer:

240

Explanation:

The sum of the exterior angles of any polygon, one per vertex, is $360 ^{\circ }$ . As each angle measures $1.5^{\circ }$ , just divide 360 by 1.5 to get the number of angles.

$360 \div 1.5=240$

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Example Question #14 : Other Polygons

What is the interior angle measure of any regular nonagon?

Possible Answers:

$140^{\circ}$

$120^{\circ}$

$200^{\circ}$

$160^{\circ}$

Correct answer:

$140^{\circ}$

Explanation:

To find the angle of any regular polygon you find the number of sides , which in this example is .

You then subtract from the number of sides yielding .

Take and multiply it by 180 degrees to yield a total number of degrees in the regular nonagon.

7*180=1260

Then to find one individual angle we divide 1260 by the total number of angles .

$\frac{1260}{9}=140$

The answer is 140 .

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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #5 : Plane Geometry

Example Question #7 : Plane Geometry

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

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

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

Example Question #11 : Plane Geometry

Example Question #1 : How To Find An Angle In A Polygon

Example Question #12 : Geometry

Example Question #13 : Other Polygons

Example Question #14 : Other Polygons

All High School Math Resources

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