Question 1

Find the area of the figure below. Give units. Show your work.

Accepted Answer

The length of the other base of the trapezoid (and the other side of the rectangle) is $8 + 2 \sqrt { 9 ^ { 2 } - 7 ^ { 2 } } \approx 19.3$ m, so the area is about $\frac { 1 } { 2 } ( 8 + 19.3 ) \cdot 7 + 19.3 \cdot 11 \approx 307.9$ m².

Question 2

What is the area of the given hexagonal region, in square centimeters? Assume that lines that look parallel are parallel and that angles that look like right angles are right angles.

Accepted Answer

A)  100 square centimeters 
B)  80 square centimeters 
C)  65 square centimeters 
D)  40 square centimeters 
E)  29 square centimeters 
A)  100 square centimeters 
B)  80 square centimeters 
C)  65 square centimeters 
D)  40 square centimeters 
E)  29 square centimeters B

Question 3

What is the length in centimeters of the base of a rectangle with diagonal of length m centimeters and width of length n centimeters?

Accepted Answer

$\sqrt { m ^ { 2 } - n ^ { 2 } }$ cm

Question 4

Find the approximate length of diagonal AC in the following right rectangular prism.

Accepted Answer

A)  15.3 centimeters 
B)  13 centimeters 
C)  9.4 centimeters 
D)  20 centimeters 
E)  48 centimeters 
A)  15.3 centimeters 
B)  13 centimeters 
C)  9.4 centimeters 
D)  20 centimeters 
E)  48 centimeters

Question 5

A plan calls for running a telephone line from P to Q to R. The line costs $7/meter. If it is feasible to run the line directly from P to R, how much money would one save?

Accepted Answer

The answer of A plan calls for running a telephone...

Question 6

An isosceles triangular right prism has the length dimensions indicated. The base of the isosceles triangle has length 12 decimeters.   
A) Find the missing lengths of the sides of the isosceles triangles.
B) Draw a net for the prism, giving the dimensions.
C) Give the volume and the surface area of the prism. Show your work.

Accepted Answer

The answer of An isosceles triangular right prism has the...

Question 7

What is the area of the right triangle shown below?

Accepted Answer

A)  6 square centimeters 
B)  10 square centimeters 
C)  12 square centimeters 
D)  20 square centimeters 
E)  There is not enough information to answer the question. 
A)  6 square centimeters 
B)  10 square centimeters 
C)  12 square centimeters 
D)  20 square centimeters 
E)  There is not enough information to answer the question.

Question 8

Find the approximate missing length in the following right rectangular prism.

Accepted Answer

The answer of Find the approximate missing length in the...

Question 9

A plan calls for running a telephone line from P to Q to R. The line costs $7/meter. If it is feasible to run the line directly from P to R, how much money would one save?

Accepted Answer

A)  $42 
B)  $105 
C)  $147 
D)  $6 
E)  $378 
A)  $42 
B)  $105 
C)  $147 
D)  $6 
E)  $378

Question 10

Find the perimeter and the area of the isosceles triangle below. Make sure to show your work. The drawing is not to scale. (Hint: The triangle can be cut into two congruent triangles.)

Accepted Answer

The answer of Find the perimeter and the area of...

Question 11

Find the approximate area and the perimeter of the shape below. The indicated point is the center of the arc.

Accepted Answer

Area = @#LAT-DLM& cm

Question 12

What is the length in centimeters of the base of a rectangle with diagonal of length m centimeters and height of length n centimeters?

Accepted Answer

A)  $\sqrt { m ^ { 2 } + n ^ { 2 } }$ 
B)  $\sqrt { m ^ { 2 } - n ^ { 2 } }$ 
C)  m - n 
D)  $\frac { m n } { 2 }$ 
E)  $\frac { m - n } { 2 }$ 
A)  $\sqrt { m ^ { 2 } + n ^ { 2 } }$ 
B)  $\sqrt { m ^ { 2 } - n ^ { 2 } }$ 
C)  m - n 
D)  $\frac { m n } { 2 }$ 
E)  $\frac { m - n } { 2 }$

Question 13

"My GPA for the first 90 units is 3.1. This semester, I'm taking 12 units and expect to get a 3.5. If I do that well, what will my overall GPA be after this semester?" (Show your work.)

Accepted Answer

The answer of "My GPA for the first 90 units...

Question 14

What does the Pythagorean Theorem assert about a right triangle with legs of lengths x centimeters and y centimeters?

Accepted Answer

The answer of What does the Pythagorean Theorem assert about...

Question 15

A) State the key ideas of measurement.
B) One of the key ideas does not apply to all quantities. Give an example, making it clear why the key idea does not apply there.

Accepted Answer

The answer of A) State the key ideas of measurement.
B)...

Question 16

What are the perimeter and area of the given figure? Use correct units. (The curved part is a semicircle.)

Accepted Answer

The perimeter is 6 @#LAT-DLM& + 20, or a

Question 17

Who had the HIGHEST average rate of speed? Show your work.
Ann, who went 450 miles in 7.5 hours
Ben, who went 20 miles in 24 minutes
Carlo, who went 175 miles in 3 hours
Daniela, who went 36 miles in 32 minutes

Accepted Answer

The answer of Who had the HIGHEST average rate of...

Question 18

Frank enlarged the dimensions of the trapezoid below by a scale factor of 150%.   
Find the following information. 
A) What is the perimeter of the original figure?
B) What is the area of the original figure?
C) What is the perimeter of the new figure?
D) What is the area of the new figure?

Accepted Answer

A) 72 centimeters
B)

Question 19

Find the area and perimeter of the shape below. The curved part is a semicircle. Show your work for credit.

Accepted Answer

The answer of Find the area and perimeter of the...

Question 20

Find the volume of a right square pyramid with each edge having length 12 centimeters. Use correct units. Show your work for credit.

Accepted Answer

From the usual right

Exam 26: Special Topics in Measurement

Find the area of the figure below. Give units. Show your work.

What is the area of the given hexagonal region, in square centimeters? Assume that lines that look parallel are parallel and that angles that look like right angles are right angles.

What is the length in centimeters of the base of a rectangle with diagonal of length m centimeters and width of length n centimeters?

Find the approximate length of diagonal AC in the following right rectangular prism.

A plan calls for running a telephone line from P to Q to R. The line costs $7/meter. If it is feasible to run the line directly from P to R, how much money would one save?

What is the area of the right triangle shown below?

Find the approximate missing length in the following right rectangular prism.

A plan calls for running a telephone line from P to Q to R. The line costs $7/meter. If it is feasible to run the line directly from P to R, how much money would one save?

Find the perimeter and the area of the isosceles triangle below. Make sure to show your work. The drawing is not to scale. (Hint: The triangle can be cut into two congruent triangles.)

Find the approximate area and the perimeter of the shape below. The indicated point is the center of the arc.

What is the length in centimeters of the base of a rectangle with diagonal of length m centimeters and height of length n centimeters?

"My GPA for the first 90 units is 3.1. This semester, I'm taking 12 units and expect to get a 3.5. If I do that well, what will my overall GPA be after this semester?" (Show your work.)

What does the Pythagorean Theorem assert about a right triangle with legs of lengths x centimeters and y centimeters?

A) State the key ideas of measurement. B) One of the key ideas does not apply to all quantities. Give an example, making it clear why the key idea does not apply there.

What are the perimeter and area of the given figure? Use correct units. (The curved part is a semicircle.)

Who had the HIGHEST average rate of speed? Show your work. Ann, who went 450 miles in 7.5 hours Ben, who went 20 miles in 24 minutes Carlo, who went 175 miles in 3 hours Daniela, who went 36 miles in 32 minutes

Frank enlarged the dimensions of the trapezoid below by a scale factor of 150%. Find the following information. A) What is the perimeter of the original figure? B) What is the area of the original figure? C) What is the perimeter of the new figure? D) What is the area of the new figure?

Find the area and perimeter of the shape below. The curved part is a semicircle. Show your work for credit.

Find the volume of a right square pyramid with each edge having length 12 centimeters. Use correct units. Show your work for credit.

Reasoning About Quantities

Numeration Systems

Understanding Whole Number Operations

Some Conventional Ways of Computing

Using Numbers in Sensible Ways

Meanings for Fractions

Computing With Fractions

Multiplicative Comparisons and Multiplicative Reasoning

Ratios, Rates, Proportions, and Percents

Integers and Other Number Systems

Number Theory

What Is Algebra

A Quantitative Approach to Algebra and Graphing

Understanding Change: Relationships Among Time, Distance, and Rate

Further Topics in Algebra and Change

Polygons

Polyhedra

Symmetry

Tessellations

Similarity

Curves, Constructions, and Curved Surfaces

Transformation Geometry

Measurement Basics

Area, Surface Area, and Volume

Counting Units Fast: Measurement Formulas

Quantifying Uncertainty

Determining More Complicated Probabilities

Introduction to Statistics and Sampling

Representing and Interpreting Data With One Variable

Dealing With Multiple Data Sets or With Multiple Variables

Variability in Samples

Special Topics in Probability

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