9.2.0: Exercises
- Page ID
- 171746
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)For the following exercises, determine the most reasonable value for each area.
kitchen floor: 16 km2, 16 m2, 16 cm2, or 16 mm2
national Park: 1,000 km2, 1,000 m2, 1,000 cm2, or 1,000 mm2
classroom table: 5 km2, 5 m2, 5 cm2, or 5 mm2
window: 9,000 km2, 9,000 m2, 9,000 cm2, or 9,000 mm2
paper napkin: 10,000 km2, 10,000 m2, 10,000 cm2, or 10,000 mm2
parking lot: 45,000 km2, 45,000 m2, 45,000 cm2, or 45,000 mm2
For the following exercises, convert the given area to the units shown.
\(700,000\,{\text{c}}{{\text{m}}^2} = \_\_\_\_\_\_\_\_\_\_\,\,{{\text{m}}^2}\)
\(24 \mathrm{~m}^2= \_\_\_\_\_\_\_\_\, \mathrm{cm}^2\)
\(985 \mathrm{~cm}^2= \_\_\_\_\_\_\_\_\,\mathrm{mm}^2\)
\(4 \mathrm{~km}^2= \_\_\_\_\_\_\_\_\,\mathrm{m}^2\)
\(0.00005 \mathrm{~km}^2= \_\_\_\_\_\_\_\_\, \mathrm{cm}^2\)
\(68,500,000{\text{ m}}{{\text{m}}^2} = \_\_\_\_\_\_\_\_\,{{\text{m}}^2}\)
\(34.5 \mathrm{~m}^2= \_\_\_\_\_\_\_\_\, \mathrm{cm}^2\)
\(7,800{\text{c}}{{\text{m}}^2} = \_\_\_\_\_\_\_\_\, {{\text{m}}^2}\)
\(34.5 \mathrm{~m}^2=\_\_\_\_\_\_\_\_\, \mathrm{cm}^2\)
\(0.05{\text{ k}}{{\text{m}}^2} = \_\_\_\_\_\_\_\_\,{{\text{m}}^2}\)
\(0.073 \mathrm{~m}^2=\_\_\_\_\_\_\_\_\, \mathrm{mm}^2\)
\(27,750{\text{ m}}{{\text{m}}^2} = \_\_\_\_\_\_\_\_\,{{\text{m}}^2}\)
For the following exercises, determine the area.
\(l = 300\) cm, \(w = 4\) m
\(A = \_\_\_\_\_\_\_\_\,{{\text{m}}^2}\)
\(l = 3,500\) mm, \(w = 0.5\) m
\(A = \_\_\_\_\_\_\_\_\,{\text{c}}{{\text{m}}^2}\)
\(l = 5.5\) km, \(w = 2,750\) m
\(A = \_\_\_\_\_\_\_\_\,{\text{k}}{{\text{m}}^2}\)
\(l = 2,400\) cm, \(w = 3.2\) m
\(A = \_\_\_\_\_\_\_\_\,{{\text{m}}^2}\)
\(l = 7\) cm, \(w = 400\) mm
\(A = \_\_\_\_\_\_\_\_\,{\text{c}}{{\text{m}}^2}\)
\(l = 2,300\) m, \(w = 4\) km
\(A = \_\_\_\_\_\_\_\_\,{\text{k}}{{\text{m}}^2}\)
\(l = 4.2\) cm, \(w = 320\) mm
\(A = \_\_\_\_\_\_\_\_\,{\text{c}}{{\text{m}}^2}\)
\(l = 5,350\) mm, \(w = 0.5\) m
\(A = \_\_\_\_\_\_\_\_\,{\text{c}}{{\text{m}}^2}\)
\(l = 1.8\) km, \(w = 2,300\) m
\(A = \_\_\_\_\_\_\_\_\,{\text{k}}{{\text{m}}^2}\)
A notebook is 200 mm by 300 mm. A sticker on the notebook cover measures 2 cm by 2 cm. How many square centimeters of the notebook cover is still visible?
A bedroom wall is 4 m by 2.5 m. A window on the wall is 1 m by 2 m. How much wallpaper is needed to cover the wall?
A wall is 5 m by 2.5 m. A picture hangs on the wall that is 600 mm by 300 mm. How much of the wall, in m2, is not covered by the picture?
What is the area of the shape that is shown?
A quilter made a design using a small square, a medium square, and a large square. What is the area of the shaded parts of the design that is shown?
A landscaper makes a plan for a walkway in a backyard, as shown. How many square meters of patio brick does the landscaper need to cover the walkway?
A painter completed a portrait. The height of the portrait is 36 cm. The width is half as long as the height. What is the area of the portrait in square meters?
A room has an area of 137.5 m2. The length of the room is 11 m. What is the width of the room?
A wall is 4.5 m long by 3 m high. A can of paint will cover an area of 10 m2. How many cans of paint are needed if each wall needs 2 coats of paint?
A soccer field is 110 meters long and 75 meters wide. If the cost of artificial turf is $30 per square meter, what is the cost of covering the soccer field with artificial turf?
A window is 150 centimeters wide and 90 centimeters high. If three times the area of the window is needed for curtain material, how much curtain material is needed in square meters?
A rectangular flower garden is 5.5 meters wide and 8.4 meters long. A path with a width of 1 meter is laid around the garden. What is the area of the path?
A dining room is 8 meters wide by 6 meters long. Wood flooring costs $12.50 per square meter. How much will it costs to install wood flooring in the dining room?