Deck 26: Special Topics in Measurement

Question 1

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

Answer 1

$\sqrt { 104 } \approx 10.2$ units

Question 2

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

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

Answer 2

15.3 centimeters

Question 3

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?

Answer 3

(21 - 15) m × $7/m = $42

Question 4

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?

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

Question 5

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

Question 6

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.)

Question 7

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?

Question 8

What is the area of the right triangle shown below?

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 9

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

Question 10

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

Question 11

What is the length of a diagonal of a square that is 12 centimeters on each side?

Question 12

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

Question 13

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

Question 14

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.

Question 15

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

Question 16

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

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 17

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.

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

Question 18

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

Question 19

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.

Question 20

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

Question 21

"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.)