Question 1

Match between columns
                        Premises: chord
radius
circumference

Accepted Answer

The Answer of A segment drawn from the center of is...

Question 2

Refer to the rectangle ABCD , shown below, where $m ( \angle 4 ) = 18 ^ { \circ }$ . 
A) $m ( \angle 1 ) = 72 ^ { \circ }$ , $m ( \angle 2 ) = 72 ^ { \circ }$  and $m ( \angle 3 ) = 18 ^ { \circ }$
B) $m ( \angle 1 ) = 18 ^ { \circ }$ , $m ( \angle 2 ) = 72 ^ { \circ }$  and $m ( \angle 3 ) = 18 ^ { \circ }$
C) $m ( \angle 1 ) = 72 ^ { \circ }$ , $m ( \angle 2 ) = 18 ^ { \circ }$  and $m ( \angle 3 ) = 72 ^ { \circ }$
D) $m ( \angle 1 ) = 18 ^ { \circ }$ , $m ( \angle 2 ) = 18 ^ { \circ }$  and $m ( \angle 3 ) = 72 ^ { \circ }$

Accepted Answer

The answer of Refer to the rectangle ABCD , shown...

Question 3

Match between columns
                        Premises: parallelogram
rhombus
rectangle

Accepted Answer

The Answer of Close the Files and Read a Record is...

Question 4

Match between columns
                        Premises: trapezoid
rhombus
rectangle
square

Accepted Answer

The Answer of Picture 2 and Picture 3 and Picture is...

Question 5

Match between columns
                        Premises: triangle
octagon
hexagon
quadrilateral
pentagon

Accepted Answer

The Answer of Picture 3 and Picture 5 and Picture is...

Question 6

Find the volume of a cone with a height of 10 centimeters and a circular base with a diameter of 9 centimeters.
A) $212.06 \mathrm {~cm} ^ { 3 }$
B) $3,316.81 \mathrm {~cm} ^ { 3 }$
C) $282.74 \mathrm {~cm} ^ { 3 }$
D) $424.12 \mathrm {~cm} ^ { 3 }$
E) $848.23 \mathrm {~cm} ^ { 3 }$

Accepted Answer

The answer of Find the volume of a cone with...

Question 7

Find the total area of the shaded figure. 
The diameters of the smaller circles are equal to 8. Use $\pi = 3.1416$ .
A) 150.8
B) 100.5
C) 301.6
D) 175.9
E) none of these

Accepted Answer

The answer of Find the total area of the shaded...

Question 8

Choose case when the triangles are similar. 
A) $\angle A = 35 ^ { \circ }$ , $\angle B = 62 ^ { \circ }$ , $\angle N = 62 ^ { \circ }$
B) $\angle A = 35 ^ { \circ }$ , $\angle M = 35 ^ { \circ }$ , $A B = 99$ , $A C = 110$ , $M N = 117$ , $M K = 130$
C) $\angle C = 83 ^ { \circ }$ , $\angle K = 83 ^ { \circ }$ , $B C = 55$ , $A C = 110$ , $N K = 68$ , $M K = 130$
D) $\angle B = 83 ^ { \circ }$ , $B C = 55$ , $A C = 110$ , $M K = 130$

Accepted Answer

In choice B, two angles of one triangle ($\angle A$ and $\angle M$) are equal to two angles of another triangle ($\angle A$ and $\angle M$), and the corresponding sides ($AB:AM$ and $AC:MK$) are in the same ratio ($99:117=110:130$). This satisfies the criteria for similarity of triangles. None of the other choices have similar triangles.

Question 9

The area of a rectangle is $250 \mathrm {~cm} ^ { 2 }$ . Its width is $11 \mathrm {~cm}$  Find its length.
A) $\text { length } = 110 \mathrm {~cm}$
B) $\text { length } = 23 \mathrm {~cm}$
C) $\text { length } = 27 \mathrm {~cm}$
D) $\text { length } = 23.5 \mathrm {~cm}$
E) $\text { length } = 20 \mathrm {~cm}$

Accepted Answer

The area of a rectangle is given by the formula: Area = length × width. Given the area is 250 cm² and the width is 11 cm, the length can be found by dividing the area by the width: length = 250 cm² / 11 cm = 22.727 cm, which rounds to approximately 23 cm.

Question 10

Refer the trapezoid KLMN below, with $\overline { K L } \| \overline { N M}$ . Find   x and y . 
A) $x = 83 ^ { \circ }$ , $y = 57 ^ { \circ }$
B) $x = 53 ^ { \circ }$ , $y = 87 ^ { \circ }$
C) $x = 57 ^ { \circ }$ , $y = 83 ^ { \circ }$
D) $x = 87 ^ { \circ }$ , $y = 53 ^ { \circ }$

Accepted Answer

The answer of Refer the trapezoid KLMN below, with \(\overline...

Question 11

Classify the following polygons:
1. 
2. 
3. 
4. 
5. 
A) Picture 1: octagon; picture 2: hexagon; picture 3: quadrilateral; picture 4: triangle and picture 5: pentagon.
B) Picture 1: quadrilateral; picture 2: octagon; picture 3: hexagon; picture 4: triangle and picture 5: pentagon.
C) Picture 1: quadrilateral; picture 2: hexagon; picture 3: octagon; picture 4: triangle and picture 5: pentagon.
D) Picture 1: quadrilateral; picture 2: pentagon; picture 3: octagon; picture 4: triangle and picture 5: hexagon.
E) Picture 1: quadrilateral; picture 2: triangle; picture 3: octagon; picture 4: hexagon and picture 5: pentagon.

Accepted Answer

The answer of Classify the following polygons:
1. 
2. 
3. 
4....

Question 12

Suppose that the length of a radius of a circle is the same as the length of a side of a square. If the circumference of the circle is 15.96 centimeters longer than the perimeter of the square, find the length of a radius of the circle. (Use 3.14 as an approximation for π .)
A) 9.28 centimeters
B) 7 centimeters
C) 6.75 centimeters
D) 7.25 centimeters
E) 2.28 centimeters

Accepted Answer

The length of the radius (r) is equal to the side of the square (s). The circumference of the circle is $2\pi r$ and the perimeter of the square is $4s$. Given that the circumference of the circle is 15.96 cm longer than the perimeter of the square, we have $2\pi r = 4s + 15.96$. Since $r = s$, we can substitute $s$ with $r$ to get $2\pi r = 4r + 15.96$. Using $3.14$ for $\pi$, we get $2(3.14)r = 4r + 15.96$, which simplifies to $6.28r = 4r + 15.96$. Solving for $r$, we subtract $4r$ from both sides to get $2.28r = 15.96$, and dividing both sides by $2.28$ gives $r = 7$ centimeters.

Question 13

Refer to trapezoid MNOP show below. Find x . 
A) 134°
B) 46°
C) 90°
D) 146°

Accepted Answer

The answer of Refer to trapezoid MNOP show below. Find...

Question 14

Find the volume of a prism whose base is a right triangle with legs 10 and 2 meters long and whose height is 7 meters.
A) $70 \mathrm {~m} ^ { 3 }$
B) $140 \mathrm {~m} ^ { 3 }$
C) $20 \mathrm {~m} ^ { 3 }$
D) $280 \mathrm {~m} ^ { 3 }$
E) $199 \mathrm {~m} ^ { 3 }$

Accepted Answer

The volume of a prism is given by the formula $V = Bh$, where $B$ is the area of the base and $h$ is the height. The base of the prism is a right triangle with legs 10 and 2 meters long, so its area is $\frac{1}{2} \times 10 \times 2 = 10$ square meters. The height of the prism is 7 meters, so its volume is $V = 10 \times 7 = 70$ cubic meters.

Question 15

Find the volume of a pyramid with a square base of 9 meters on each side and a height of 12 meters.
A) $324 \mathrm {~m} ^ { 3 }$
B) $108 \mathrm {~m} ^ { 3 }$
C) $973 \mathrm {~m} ^ { 3 }$
D) $1,296 \mathrm {~m} ^ { 3 }$
E) none of these

Accepted Answer

The volume of a pyramid is given by the formula V = (1/3) * B * h, where B is the area of the base and h is the height. In this case, the base is a square with a side length of 9 meters, so the area of the base is 9^2 = 81 square meters. The height of the pyramid is 12 meters. Therefore, the volume of the pyramid is V = (1/3) * 81 * 12 = 324 cubic meters.

Question 16

In the figure below, $A B \| C D$ . Are $\triangle A O B$  and $$\triangle C O D$$  similar triangles? 
A) Yes
B) No

Accepted Answer

The answer of In the figure below, \(A B \|...

Question 17

The north wall of a barn is a rectangle 60 feet high and 55 feet long. There are five windows in the wall, each 4 by 4 feet. If a gallon of paint will cover 400 square feet, how many gallons of paint must the painter buy to paint the wall?
A) 9
B) 8
C) 10
D) 11
E) none of these

Accepted Answer

The answer of The north wall of a barn is...

Question 18

Find the area of the shaded part of the figure if $a = 6$ , $b = 7$ , $$c = 4$$ 
A) 49
B) 24
C) 108
D) 66
E) none of these

Accepted Answer

The answer of Find the area of the shaded part...

Question 19

The angle a shown in the illustration is $30 ^ { \circ }$ Find b , if the two triangles are similar. 
A) $15 ^ { \circ }$
B) $60 ^ { \circ }$
C) $30 ^ { \circ }$
D) $16 ^ { \circ }$
E) none of these

Accepted Answer

The answer of The angle a shown in the illustration...

Question 20

Refer the trapezoid shown below. Find x . 
A) 42°
B) 138°
C) 142°
D) 125°

Accepted Answer

The answer of Refer the trapezoid shown below. Find x...

Quiz 9: An Introduction to Geometry

Match the corresponding statements.

Classify the following quadrilaterals. Match the shape with the name. 1. 2. 3. 4.

Classify the following polygons. Match the pictures with the names. 1. 2. 3. 4. 5. Choose the correct letter for each question.

Find the volume of a cone with a height of 10 centimeters and a circular base with a diameter of 9 centimeters.

Find the total area of the shaded figure. $Find the total area of the shaded figure. The diameters of the smaller circles are equal to 8. Use \pi = 3.1416 . A) 150.8 B) 100.5 C) 301.6 D) 175.9 E) none of these$ The diameters of the smaller circles are equal to 8. Use $\pi = 3.1416$ .

The area of a rectangle is $250 \mathrm {~cm} ^ { 2 }$ . Its width is $11 \mathrm {~cm}$ Find its length.

Classify the following polygons: 1. 2. 3. 4. 5.

Suppose that the length of a radius of a circle is the same as the length of a side of a square. If the circumference of the circle is 15.96 centimeters longer than the perimeter of the square, find the length of a radius of the circle. (Use 3.14 as an approximation for π .)

Refer to trapezoid MNOP show below. Find x .

Find the volume of a prism whose base is a right triangle with legs 10 and 2 meters long and whose height is 7 meters.

Find the volume of a pyramid with a square base of 9 meters on each side and a height of 12 meters.

In the figure below, $A B \| C D$ . Are $\triangle A O B$ and $\triangle C O D$ similar triangles? $In the figure below, A B \| C D . Are \triangle A O B and \triangle C O D similar triangles? A) Yes B) No$

The north wall of a barn is a rectangle 60 feet high and 55 feet long. There are five windows in the wall, each 4 by 4 feet. If a gallon of paint will cover 400 square feet, how many gallons of paint must the painter buy to paint the wall?

Find the area of the shaded part of the figure if $a = 6$ , $b = 7$ , $c = 4$

The angle a shown in the illustration is $30 ^ { \circ }$ Find b , if the two triangles are similar. $The angle a shown in the illustration is 30 ^ { \circ } Find b , if the two triangles are similar. A) 15 ^ { \circ } B) 60 ^ { \circ } C) 30 ^ { \circ } D) 16 ^ { \circ } E) none of these$

Refer the trapezoid shown below. Find x .

Quiz 9: An Introduction to Geometry

Match the corresponding statements.

Refer to the rectangle ABCD , shown below, where m(∠4) =18∘m ( \angle 4 ) = 18 ^ { \circ }m(∠4) =18∘ .

Classify the following quadrilaterals. Match the shape with the name. 1. 2. 3. 4.

Classify the following polygons. Match the pictures with the names. 1. 2. 3. 4. 5. Choose the correct letter for each question.

Find the volume of a cone with a height of 10 centimeters and a circular base with a diameter of 9 centimeters.

Find the total area of the shaded figure. The diameters of the smaller circles are equal to 8. Use π=3.1416\pi = 3.1416π=3.1416 .

Choose case when the triangles are similar.

The area of a rectangle is 250 cm2250 \mathrm {~cm} ^ { 2 }250 cm2 . Its width is 11 cm11 \mathrm {~cm}11 cm Find its length.

Refer the trapezoid KLMN below, with KL‾∥NM‾\overline { K L } \| \overline { N M}KL∥NM . Find x and y .