Question 1

Find the missing side lengths in the triangle. Give the exact answer and then an approximation to two decimal places, when appropriate.

Accepted Answer

A)  $x = 10 \sqrt { 3 } \approx 17.35 , h = 20$ 
B)  $x = 10 \sqrt { 3 } \approx 17.32 , h = 20$ 
C)  $x = 20 , h = 10 \sqrt { 3 } \approx 17.32$ 
D)  $x = 21 , h = 10 \sqrt { 3 } \approx 17.35$ 
E)  $x = 10 \sqrt { 3 } \approx 17.32 , h = 21$ 
A)  $x = 10 \sqrt { 3 } \approx 17.35 , h = 20$ 
B)  $x = 10 \sqrt { 3 } \approx 17.32 , h = 20$ 
C)  $x = 20 , h = 10 \sqrt { 3 } \approx 17.32$ 
D)  $x = 21 , h = 10 \sqrt { 3 } \approx 17.35$ 
E)  $x = 10 \sqrt { 3 } \approx 17.32 , h = 21$ B

Question 2

Match between columns
                        Premises: pentagon
octagon
hexagon
quadrilateral
triangle

Accepted Answer

The Answer of Picture 1 and Picture 2 and Picture is...

Question 3

The illustration shows a block that is suspended with two ropes, one of which is horizontal. The weight of the block is $A = 68$ . Which numbered angle in the illustration is acute?

Accepted Answer

A)  3 
B)  2 
C)  1 
A)  3 
B)  2 
C)  1 B

Question 4

Refer the trapezoid shown below. Find x .

Accepted Answer

A)  42° 
B)  138° 
C)  142° 
D)  125° 
A)  42° 
B)  138° 
C)  142° 
D)  125°

Question 5

In the figure below, $a = 10$ , $b = 5$ , and  $c = 45$ .
What is the measure of angle y ?

Accepted Answer

A)  99 
B)  189 
C)  90 
D)  9 
E)  none of these 
A)  99 
B)  189 
C)  90 
D)  9 
E)  none of these

Question 6

FIGURE 1   
The right triangle ABC is shown in Figure 1. Find the length of the missing side by using the Pythagorean Theorem, if $a = 12$ ft and $b = 16$ ft. 
c = __________ ft

Accepted Answer

The answer of FIGURE 1   
The right triangle...

Question 7

The tree in the illustration casts a shadow $c = 6$  feet long, while a person $a = 6$  feet tall casts a shadow $b = 4$  feet long. 
Find the height of the tree.

Accepted Answer

A)  $\frac { 3 } { 12 }$ 
B)  15 
C)  $\frac { 1 } { 9 }$ 
D)  9 
E)  none of these 
A)  $\frac { 3 } { 12 }$ 
B)  15 
C)  $\frac { 1 } { 9 }$ 
D)  9 
E)  none of these

Question 8

Use the dimensions in the illustration to find w , the width of the river, if $a = 16$ , $b = 20$ , and $$c = 80$$ .

Accepted Answer

A)  64 
B)  80 
C)  $\frac { 1 } { 27 }$ 
D)  $\frac { 36 } { 5 }$ 
E)  none of these 
A)  64 
B)  80 
C)  $\frac { 1 } { 27 }$ 
D)  $\frac { 36 } { 5 }$ 
E)  none of these

Question 9

Refer to the illustration. Find $C$  if $a = 4$  and $b = 3$ .

Accepted Answer

A)  5 
B)  $\sqrt { 60 }$ 
C)  $\sqrt { 18 }$ 
D)  $\sqrt { 17 }$ 
E)  7 
A)  5 
B)  $\sqrt { 60 }$ 
C)  $\sqrt { 18 }$ 
D)  $\sqrt { 17 }$ 
E)  7

Question 10

In the figure below, angle $$a = 51 ^ { \circ }$$ . Find $\chi$ .

Accepted Answer

A)  166 
B)  39 
C)  129 
D)  78 
E)  64 
A)  166 
B)  39 
C)  129 
D)  78 
E)  64

Question 11

In isosceles triangle $R S T$ , $\overline { R S } \cong \overline { S T }$ . If $m \angle T = 2 ( x + 3 )$ and $m \angle S = 3 x$ , find the value of x .

Accepted Answer

A)  $x = 24$ 
B)  $x = 32$ 
C)  $x = 46$ 
D)  $x = 58$ 
A)  $x = 24$ 
B)  $x = 32$ 
C)  $x = 46$ 
D)  $x = 58$

Question 12

Find the area of the shaded part of the figure if $a = 18$ , $$b = 5$$ .

Accepted Answer

A)  90 
B)  180 
C)  45 
D)  14 
E)  none of these 
A)  90 
B)  180 
C)  45 
D)  14 
E)  none of these

Question 13

Find the volume of a sphere with a radius of 10 inches.

Accepted Answer

A)  $1,333.33 \text { in. } ^ { 3 }$ 
B)  $16,755.16 \mathrm { in } ^ { 3 }$ 
C)  $12,566.37 \mathrm { in } ^ { 3 }$ 
D)  $418.88 \mathrm { in } ^ { 3 }$ 
E)  $4,188.79 \mathrm { in } . ^ { 3 }$ 
A)  $1,333.33 \text { in. } ^ { 3 }$ 
B)  $16,755.16 \mathrm { in } ^ { 3 }$ 
C)  $12,566.37 \mathrm { in } ^ { 3 }$ 
D)  $418.88 \mathrm { in } ^ { 3 }$ 
E)  $4,188.79 \mathrm { in } . ^ { 3 }$

Question 14

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

Accepted Answer

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)  $848.23 \mathrm {~cm} ^ { 3 }$ 
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)  $848.23 \mathrm {~cm} ^ { 3 }$

Question 15

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

Accepted Answer

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 
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

Question 16

Find the area of the shaded part of the figure if $a = 8$ , $b = 9$ , $c = 4$ .

Accepted Answer

A)  72 
B)  30 
C)  176 
D)  104 
E)  none of these 
A)  72 
B)  30 
C)  176 
D)  104 
E)  none of these

Question 17

In the figure below, $a = 10$ , $b = 5$ , $c = 8$ , and $d = 43$ . Find x .

Accepted Answer

A)  25 
B)  20 
C)  19 
D)  24 
E)  18 
A)  25 
B)  20 
C)  19 
D)  24 
E)  18

Question 18

In the figure below, $$a = 128$$ . Find x and y .

Accepted Answer

A)  $x = 52$ , $y = 128$ 
B)  $x = 128$ , $y = 128$ 
C)  $x = 128$ , $y = 52$ 
A)  $x = 52$ , $y = 128$ 
B)  $x = 128$ , $y = 128$ 
C)  $x = 128$ , $y = 52$

Question 19

Look at the illustration and match each angle with its type. $$\angle 1 = 54 ^ { \circ }$$   and $\angle 2 = 36 ^ { \circ }$ .  
-obtuse

Accepted Answer

A)  AGC 
B)  FGD 
C)  BGE 
D)  BGA 
A)  AGC 
B)  FGD 
C)  BGE 
D)  BGA

Question 20

Find the area of the circle to the nearest tenth, if $\pi = 3.14$ and a = 10 in.   
__________ in $2$

Accepted Answer

The answer of Find the area of the circle to...

Find the missing side lengths in the triangle. Give the exact answer and then an approximation to two decimal places, when appropriate.

The illustration shows a block that is suspended with two ropes, one of which is horizontal. The weight of the block is $A = 68$ . Which numbered angle in the illustration is acute?

Refer the trapezoid shown below. Find x .

In the figure below, $a = 10$ , $b = 5$ , and $c = 45$ . What is the measure of angle y ?

FIGURE 1 The right triangle ABC is shown in Figure 1. Find the length of the missing side by using the Pythagorean Theorem, if $a = 12$ ft and $b = 16$ ft. c = __________ ft

The tree in the illustration casts a shadow $c = 6$ feet long, while a person $a = 6$ feet tall casts a shadow $b = 4$ feet long. Find the height of the tree.

Use the dimensions in the illustration to find w , the width of the river, if $a = 16$ , $b = 20$ , and $c = 80$ .

Refer to the illustration. Find $C$ if $a = 4$ and $b = 3$ .

In the figure below, angle $a = 51 ^ { \circ }$ . Find $\chi$ . $In the figure below, angle a = 51 ^ { \circ } . Find \chi .$

In isosceles triangle $R S T$ , $\overline { R S } \cong \overline { S T }$ . If $m \angle T = 2 ( x + 3 )$ and $m \angle S = 3 x$ , find the value of x .

Find the area of the shaded part of the figure if $a = 18$ , $b = 5$ .

Find the volume of a sphere with a radius of 10 inches.

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

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

Find the area of the shaded part of the figure if $a = 8$ , $b = 9$ , $c = 4$ .

In the figure below, $a = 10$ , $b = 5$ , $c = 8$ , and $d = 43$ . Find x .

In the figure below, $a = 128$ . Find x and y .

Look at the illustration and match each angle with its type. $\angle 1 = 54 ^ { \circ }$ and $\angle 2 = 36 ^ { \circ }$ . $Look at the illustration and match each angle with its type. \angle 1 = 54 ^ { \circ } and \angle 2 = 36 ^ { \circ } . -obtuse$ -obtuse

Find the area of the circle to the nearest tenth, if $\pi = 3.14$ and a = 10 in. $Find the area of the circle to the nearest tenth, if \pi = 3.14 and a = 10 in. in 2$ in $2$

Whole Numbers

The Integers

Fractions and Mixed Numbers

Decimals

Ratio, Proportion, and Measurement

Percent

Graphs, Statistics, and Probability

An Introduction to Algebra

Filters

Exam 9: An Introduction to Geometry

Find the missing side lengths in the triangle. Give the exact answer and then an approximation to two decimal places, when appropriate.

The illustration shows a block that is suspended with two ropes, one of which is horizontal. The weight of the block is A=68A = 68A=68 . Which numbered angle in the illustration is acute?

Refer the trapezoid shown below. Find x .

In the figure below, a=10a = 10a=10 , b=5b = 5b=5 , and c=45c = 45c=45 . What is the measure of angle y ?

FIGURE 1 The right triangle ABC is shown in Figure 1. Find the length of the missing side by using the Pythagorean Theorem, if a=12a = 12a=12 ft and b=16b = 16b=16 ft. c = __________ ft

The tree in the illustration casts a shadow c=6c = 6c=6 feet long, while a person a=6a = 6a=6 feet tall casts a shadow b=4b = 4b=4 feet long. Find the height of the tree.

Use the dimensions in the illustration to find w , the width of the river, if a=16a = 16a=16 , b=20b = 20b=20 , and c=80c = 80c=80 .

Refer to the illustration. Find CCC if a=4a = 4a=4 and b=3b = 3b=3 .

In the figure below, angle a=51∘a = 51 ^ { \circ }a=51∘ . Find χ\chiχ .

In isosceles triangle RSTR S TRST , RS‾≅ST‾\overline { R S } \cong \overline { S T }RS≅ST . If m∠T=2(x+3)m \angle T = 2 ( x + 3 )m∠T=2(x+3) and m∠S=3xm \angle S = 3 xm∠S=3x , find the value of x .

Find the area of the shaded part of the figure if a=18a = 18a=18 , b=5b = 5b=5 .

Find the volume of a sphere with a radius of 10 inches.

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

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

Find the area of the shaded part of the figure if a=8a = 8a=8 , b=9b = 9b=9 , c=4c = 4c=4 .

In the figure below, a=10a = 10a=10 , b=5b = 5b=5 , c=8c = 8c=8 , and d=43d = 43d=43 . Find x .

In the figure below, a=128a = 128a=128 . Find x and y .

Look at the illustration and match each angle with its type. ∠1=54∘\angle 1 = 54 ^ { \circ }∠1=54∘ and ∠2=36∘\angle 2 = 36 ^ { \circ }∠2=36∘ . -obtuse

Find the area of the circle to the nearest tenth, if π=3.14\pi = 3.14π=3.14 and a = 10 in. __________ in 222

Whole Numbers

The Integers

Fractions and Mixed Numbers

Decimals

Ratio, Proportion, and Measurement

Percent

Graphs, Statistics, and Probability

An Introduction to Algebra

Filters

The illustration shows a block that is suspended with two ropes, one of which is horizontal. The weight of the block is $A = 68$ . Which numbered angle in the illustration is acute?

In the figure below, $a = 10$ , $b = 5$ , and $c = 45$ . What is the measure of angle y ?

FIGURE 1 The right triangle ABC is shown in Figure 1. Find the length of the missing side by using the Pythagorean Theorem, if $a = 12$ ft and $b = 16$ ft. c = __________ ft

The tree in the illustration casts a shadow $c = 6$ feet long, while a person $a = 6$ feet tall casts a shadow $b = 4$ feet long. Find the height of the tree.

Use the dimensions in the illustration to find w , the width of the river, if $a = 16$ , $b = 20$ , and $c = 80$ .

Refer to the illustration. Find $C$ if $a = 4$ and $b = 3$ .

In the figure below, angle $a = 51 ^ { \circ }$ . Find $\chi$ . $In the figure below, angle a = 51 ^ { \circ } . Find \chi .$

In isosceles triangle $R S T$ , $\overline { R S } \cong \overline { S T }$ . If $m \angle T = 2 ( x + 3 )$ and $m \angle S = 3 x$ , find the value of x .

Find the area of the shaded part of the figure if $a = 18$ , $b = 5$ .

Find the area of the shaded part of the figure if $a = 8$ , $b = 9$ , $c = 4$ .

In the figure below, $a = 10$ , $b = 5$ , $c = 8$ , and $d = 43$ . Find x .

In the figure below, $a = 128$ . Find x and y .

Look at the illustration and match each angle with its type. $\angle 1 = 54 ^ { \circ }$ and $\angle 2 = 36 ^ { \circ }$ . $Look at the illustration and match each angle with its type. \angle 1 = 54 ^ { \circ } and \angle 2 = 36 ^ { \circ } . -obtuse$ -obtuse

Find the area of the circle to the nearest tenth, if $\pi = 3.14$ and a = 10 in. $Find the area of the circle to the nearest tenth, if \pi = 3.14 and a = 10 in. in 2$ in $2$