2.12: Exercises

Last updated
Save as PDF

Page ID: 113134

$ \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}}$

2.1 Basic Geometric Concepts

1. Classify the angle below as acute, obtuse, or right.

$clipboard_ea48ccb13e941befbd2514bbc79d4cc9b.png$

2. Classify the angle below as acute, obtuse, or right.

$clipboard_e235838468eb6c298b4ad1aa77c0ee428.png$

3. Classify the angle shown as acute, obtuse, or right.

$clipboard_ebc186a3bcf36db228d1c241ee08a2491.png$

2.2 Properties of Angles

Use the picture below to answer the following questions. Note, ∠AOF is a right angle.

$clipboard_e6387442895240094d68bc05f07439e3f.png$

a) Which angle is supplementary to ∠BOC?

b) Which angle is complementary to ∠BOC?

c) What is the measure of ∠EOF?

d) What is the measure of ∠AOE?

e) What is the measure of ∠BOF?

2.3 Triangles

1. Find the unknown angle measure.

$clipboard_e7c47560535ebea783537bc5c2b4a87b6.png$

2. Find the unknown angle measure.

$clipboard_e96ad887a484844449f3c3fb2bb87b2d6.png$

3. Find the unknown angle measure.

$clipboard_e52a2458dda7a98fb443dcd0c7fc72b2c.png$

4. Find the unknown angle measure.

$clipboard_e2e0e98562bd4605cb192192ffda31863.png$

5. Find the unknown angle measures.

$clipboard_e7f07e49345e1049790c529a2a443aca0.png$

6. Find the unknown angle measure.

$clipboard_ef1763d273ab3d9f5a1b5d1981dcb6454.png$

2.4 The Pythagorean Theorem

Find the length of the hypotenuse of the given right triangle pictured below. Round to two decimal places.

$clipboard_e140963f309a15b859842e57f7b2232ce.png$

2. Find the length of the leg $x$. Enter the exact value, not a decimal approximation.

$clipboard_e56fe15ceef9a1fc945f9a13b74cc303a.png$

2.5 Quadrilaterals

Find type of quadrilateral is the figure shown below.

$clipboard_eee5ffb951d769773aa62a1a289600ba0.png$

2.6 Perimeter and Area

Find the perimeter of the figure pictured below.

$clipboard_e4aefdfbeb68951c9330644097190bb28.png$

2. Find the perimeter of the rectangle pictured below.

$clipboard_e56c02341f1a23097a7ef27fb8ab287bd.png$

3. Find the perimeter of the parallelogram shown below.

$clipboard_eee5ffb951d769773aa62a1a289600ba0.png$

4. Find the area of the rectangle pictured below.

$clipboard_ef3cfdf2bf62e1b71b5bfb83430037f13.png$

5. Find the area of the figure pictured below and state the correct units.

$clipboard_e82856fe51e9b0790ce910f6df9258272.png$

6. Find the area of the parallelogram shown below.

$clipboard_ee5fe00dae28c99bc4a18207e5a70499d.png$

7. The area of a triangle can be found using the formula: $\text{Area } = \dfrac{1}{2} \cdot \text{base} \cdot \text{height}$. Find the area of the triangle pictured below, where the measurements are given in meters (m).

$clipboard_e878643b7bbd30f45e5bb56cd27e2bcf0.png$

2.7 Circles

Find the circumference of the circle pictured below. Round your answer to the nearest hundredth.

$clipboard_e11b3602b9f83f1d21bf3f12d984a2f69.png$

2. Find the circumference of the circle pictured below. Round your answer to the nearest hundredth.

$clipboard_e9c52cbd8dc39d1ab1c113968e5bb5dce.png$

3. Find the area of the circle pictured below. Round your answer to the nearest hundredth.

$clipboard_e1b68fe322566ffc2f5c28b62cdc356b5.png$

4. Find the area of the shaded area. Round your answer to the nearest tenth.

$clipboard_e7453e7fbef849482225c4a3610761329.png$

2.8 Solids

1. Match the formula for each volume to the figure to which it applies.

Figure	Volume
Right Circular Cylinder	A. $V = \dfrac{4}{3} \pi r^3$
Rectangular Solid	B. $V = \pi r^2 h$
Sphere	C. $V = l \cdot w \cdot h$

2. The volume of a cylinder with height $h$ and radius $r$ can be found using the formula $V = \pi r^2 h$. Sketch a cylinder with radius $7$ feet and height $4$ feet, then find the volume and select the correct units. Round your answer to the nearest tenth.

3. The volume of a cone with height $h$ and radius $r$ can be found using the formula $V = \dfrac{1}{3} \pi r^2 h$. Sketch a cone with radius $9$ feet and height $3$ feet, then find the volume and select the correct units. Round your answer to the nearest tenth.

4. A sports ball has a diameter of $26 \text{ cm}$. Find the volume of the ball and select the correct units. Round your answer to 2 decimal places.