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高的h School Math : Geometry

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

What is the perimeter of a regular hendecagon with a side length of 32?

Possible Answers:

320

334

384

352

Correct answer:

352

Explanation:

To find the perimeter of a regular hendecagon you must first know the number of sides in a hendecagon is 11.

When you know the number of sides of a regular polygon to find the perimeter you must multiply the side length by the number of sides.

在这种情况下 11*32=352 .

The answer for the perimeter is 352 .

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

All segments of the polygon meet at right angles (90 degrees). The length of segment $\overline{AB}$ is 10. The length of segment $\overline{BC}$ is 8. The length of segment $\overline{DE}$ is 3. The length of segment $\overline{GH}$ is 2.

Find the perimeter of the polygon.

Possible Answers:

$\dpi{100} \small 40$

$\dpi{100} \small 44$

$\dpi{100} \small 42$

$\dpi{100} \small 48$

$\dpi{100} \small 46$

Correct answer:

$\dpi{100} \small 46$

Explanation:

The perimeter of the polygon is 46. Think of this polygon as a rectangle with two of its corners "flipped" inwards. This "flipping" changes the area of the rectangle, but not its perimeter; therefore, the top and bottom sides of the original rectangle would be 12 units long $\dpi{100} \small (10+2=12)$ . The left and right sides would be 11 units long $\dpi{100} \small (8+3=11)$ . Adding all four sides, we find that the perimeter of the recangle (and therefore, of this polygon) is 46.

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Example Question #3 :How To Find The Perimeter Of A Polygon

What is the perimeter of a regular nonagon with a side length of?

Possible Answers:

120

150

105

135

Correct answer:

135

Explanation:

To find the perimeter of a regular polygon, we take the length of each side,, and multiply it by the number of sides,.

P=s*l

In a nonagon the number of sides is, and in this example the side length is.

P=9*15=135

The perimeter is 135 .

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Example Question #4 :How To Find The Perimeter Of A Polygon

Find the perimeter of the following octagon:

Possible Answers:

$96\ m$

$86\ m$

$56\ m$

$76\ m$

$66\ m$

Correct answer:

$96\ m$

Explanation:

The formula for the perimeter of an octagon is P = 8(side) .

Plugging in our values, we get:

$P = 8(12\ m)$

$P = 96\ m$

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Example Question #1 :Plane Geometry

What is the area of a regular heptagon with an apothem of 4 and a side length of 6?

Possible Answers:

Correct answer:

Explanation:

What is the area of a regular heptagon with an apothem of 4 and a side length of 6?

To find the area of any polygon with the side length and the apothem we must know the equation for the area of a polygon which is

First, we must calculate the perimeter using the side length.

我们找到一个正多边形的周长the length of each side and multiply it by the number of sides.

In a heptagon the number of sides is 7 and in this example the side length is 6 so

The perimeter is.

Then we plug in the numbers for the apothem and perimeter into the equation yielding

We then multiply giving us the area of.

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

What is the area of a regular decagon with an apothem of 15 and a side length of 25?

Possible Answers:

1875

3750

2750

375

Correct answer:

1875

Explanation:

To find the area of any polygon with the side length and the apothem we must know the equation for the area of a polygon which is

First, we must calculate the perimeter using the side length.

我们找到一个正多边形的周长the length of each side and multiply it by the number of sides.

In a decagon the number of sides is 10 and in this example the side length is 25 so 25*10=250

The perimeter is 250 .

Then we plug in the numbers for the apothem and perimeter into the equation yielding $Area\:of\:Polygon=\frac{1}{2}(250)15$

We then multiply giving us the area of 1875 .

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Example Question #3 :Geometry

What is the area of a regular heptagon with an apothem of和一个勒ngth of?

Possible Answers:

224

112

Correct answer:

112

Explanation:

To find the area of any polygon with the side length and the apothem we must know the equation for the area of a polygon which is

We must then calculate the perimeter using the side length.

我们找到一个正多边形的周长the length of each side and multiply it by the number of sides.

In a heptagon the number of sidesisand in this example the side length isso 8*7=56

The perimeter is 56.

Then we plug in the numbers for the apothem and perimeter into the equation yielding $Area=(\frac{1}{2})(56)(4)$

We then multiply giving us the area of 112 .

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Example Question #4 :Geometry

Find the area of the shaded region:

Screen_shot_2014-02-27_at_6.53.35_pm

Possible Answers:

$75\pi m^2$

75m^2

$100m^2 - 25\pi m^2$

$100m^2 + 25\pi m^2$

$100\pi m^2 - 25m^2$

Correct answer:

$100m^2 - 25\pi m^2$

Explanation:

To find the area of the shaded region, you must subtract the area of the circle from the area of the square.

The formula for the shaded area is:

$A=A_{square}-A_{circle}$

$A = (s)^2 - \pi(r)^2$ ,

whereis the side of the square andis the radius of the circle.

Plugging in our values, we get:

$A = (10m)^2 - \pi(5m)^2$

$A = 100m^2 - 25\pi m^2$

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Example Question #5 :Geometry

Find the area of the shaded region:

Screen_shot_2014-03-01_at_9.02.03_pm

Possible Answers:

$9\pi - 24cm^2$

$9\pi - 9cm^2$

$6\pi - 9cm^2$

$9\pi - 18cm^2$

$6\pi - 18cm^2$

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:

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

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

Whereis the radius of the circle, part is the fraction of the circle,is the base of the triangle, andis 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 #6 :Geometry

Find the area of the shaded region:

Screen_shot_2014-03-01_at_9.04.49_pm

Possible Answers:

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

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

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

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

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

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:

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

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

Whereis the radius of the circle, part is the fraction of the circle, andis 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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高的h School Math : Geometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

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

Example Question #3 :How To Find The Perimeter Of A Polygon

Example Question #4 :How To Find The Perimeter Of A Polygon

Example Question #1 :Plane Geometry

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

Example Question #3 :Geometry

Example Question #4 :Geometry

Example Question #5 :Geometry

Example Question #6 :Geometry

All High School Math Resources

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