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ACT Math : Plane Geometry

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Example Questions

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

A circle has an area of 36π inches. What is the radius of the circle, in inches?

Possible Answers:

Correct answer:

Explanation:

We know that the formula for the area of a circle is πr². Therefore, we must set 36π equal to this formula to solve for the radius of the circle.

36π = πr²

36 = r²

6 = r

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Example Question #3 : How To Find The Length Of A Radius

Circle X is divided into 3 sections: A, B, and C. The 3 sections are equal in area. If the area of section C is 12π, what is the radius of the circle?

Act_math_170_02

Circle X

Possible Answers:

√12

Correct answer:

Explanation:

Find the total area of the circle, then use the area formula to find the radius.

Area of section A = section B = section C

Area of circle X = A + B + C = 12π+ 12π + 12π = 36π

Area of circle = where r is the radius of the circle

36π = πr²

36 = r²

√36 = r

6 = r

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Example Question #4 : How To Find The Length Of A Radius

The specifications of an official NBA basketball are that it must be 29.5 inches in circumference and weigh 22 ounces. What is the approximate radius of the basketball?

Possible Answers:

5.43 inches

9.39 inches

14.75 inches

4.70 inches

3.06 inches

Correct answer:

4.70 inches

Explanation:

To Find your answer, we would use the formula: C=2πr. We are given that C = 29.5. Thus we can plug in to get [29.5]=2πr and then multiply 2π to get 29.5=(6.28)r. Lastly, we divide both sides by 6.28 to get 4.70=r. (The information given of 22 ounces is useless)

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Example Question #111 : Circles

A circle with center (8, –5) is tangent to the y-axis in the standard (x,y) coordinate plane. What is the radius of this circle?

Possible Answers:

Correct answer:

Explanation:

For the circle to be tangent to the y-axis, it must have its outer edge on the axis. The center is 8 units from the edge.

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Example Question #1 : Radius

A circle has an area of $49\pi \ in^{2}$ . What is the radius of the circle, in inches?

Possible Answers:

49 inches

7 inches

16 inches

24.5 inches

14 inches

Correct answer:

7 inches

Explanation:

We know that the formula for the area of a circle is πr². Therefore, we must set 49π equal to this formula to solve for the radius of the circle.

49π = πr²

49 = r²

7 = r

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Example Question #6 : How To Find The Length Of A Radius

A circle has a circumference of $32\pi\:ft$ . What is the radius of the circle, in feet?

Possible Answers:

$8\:ft$

$32\:ft$

$16\:ft$

$8\pi\:ft$

$16\pi\:ft$

Correct answer:

$16\:ft$

Explanation:

To answer this question we need to find the radius of the circle given the circumference of $32\pi$ .

The equation for a circle's circumference is:

$circumference=\pi \cdot diameter$

We can plug our circumference into this equation to find the diameter.

$circumference=\pi \cdot diameter$

$32\pi=\pi\cdot diameter$

We can now divide both sides by $\Pi$

$\frac{32\pi }{\pi }=\frac{\pi \cdot diameter}{\pi }$

32=diameter

So our diameter is $32\:ft$ . To find the radius from the diameter, we use the following equation:

$radius=\frac{diameter}{2}$

So, for this data:

$radius=\frac{32}{2}=16$

Therefore, the radius of our circle is $16\:ft$ .

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Example Question #1 : Plane Geometry

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:

$\dpi{100} \small 44$

$\dpi{100} \small 48$

$\dpi{100} \small 46$

$\dpi{100} \small 40$

$\dpi{100} \small 42$

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 #2 : How To Find The Perimeter Of A Polygon

In the figure below, each pair of intersecting line segments forms a right angle, and all the lengths are given in feet. What is the perimeter, in feet, of the figure?

Quad

Possible Answers:

Correct answer:

Explanation:

Fill in the missing sides by thinking about the entire figure as a big rectangle. In the figure below, the large rectangle is outlined in blue and the missing numbers are supplied in red.

Quad

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Example Question #595 : Plane Geometry

What is the perimeter of a regular, $\textup{13-sided}$ polygon with a side length of $4\textup{cm}$ ?

Possible Answers:

$\textup{56cm}$

$\textup{44cm}$

$\textup{52cm}$

$\textup{4cm}$

$\textup{50cm}$

Correct answer:

$\textup{52cm}$

Explanation:

To find the perimeter of an -sided polygon with a side length of , simply multiply the side length by the number of sides:
$4\textup{cm}*13=52\textup{cm}$

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Example Question #591 : Act Math

Polygon ABCDEFGHI is a regular nine-sided polygon, or nonagon, with perimeter 500. Which choice comes closest to the length of diagonal $\overline{AD}$ ?

Possible Answers:

120

150

160

130

140

Correct answer:

140

Explanation:

Congruent sides $\overline{AB}$ , $\overline{BC}$ , and $\overline{CD}$ , and the diagonal $\overline{AD}$ form an isosceles trapezoid.

$\angle ABC$ and $\angle BCD$ . being angles of a nine-sided regular polygon, have measure

$m \angle ABC = m\angle BCDC = \frac{180 ^{\circ } (9-2)}{9} =140^{\circ }$

The other two angles are supplementary to these:

$m \angle DAB = m \angle ADC = 180 ^{\circ }- 140^{\circ } = 40 ^{\circ }$

The length of one side of the nonagon is one-ninth of 500, so

$AB = BC =CD= \frac{500}{9} \approx 55.56$

The trapezoid formed is below (figure NOT drawn to scale):

Thingy

Altitudes $\overline{BM}$ and $\overline{CN}$ to the base have been drawn, so

AD = AM + MN + ND

AD = AM + BC+ AM

$AD = 2 \cdot AM + 55.56$

$\frac{AM}{AB} = \cos 40^{ \circ}$

$AM=AB \cos 40^{ \circ} \approx 55.56 \cdot 0.7660 \approx 42.56$

$AD \approx 2 \cdot 42.56 + 55.56 \approx 140.68$

This makes 140 the best choice.

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ACT Math : Plane Geometry

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

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

Example Question #3 : How To Find The Length Of A Radius

Example Question #4 : How To Find The Length Of A Radius

Example Question #111 : Circles

Example Question #1 : Radius

Example Question #6 : How To Find The Length Of A Radius

Example Question #1 : Plane Geometry

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

Example Question #595 : Plane Geometry

Example Question #591 : Act Math

All ACT Math Resources

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