edututorAi

td0715

23.04.2020 •

Mathematics

For each problem, use the formula for area of a polygon A = 12 ap , where a is the length of the
apothem and p is the perimeter of the polygon, to find the area of the polygon.
Show the exact values of a and p on your figure and give your answers as exact values - no rounding – no decimals. Show all your work clearly. All polygons represented are regular polygons.

For each problem, use the formula for area of a polygon A = 12 ap , where a is the length of the apo

Solved

Show answers

Ответ:

ToxicMonkey

25.01.2022

Mathematics

Part 1) Triangle: $P=24\sqrt{3}\ in$ and $A=48\sqrt{3}\ in^2$

Part 2) Square: $P=40\sqrt{2}\ ft$ and $A=200\ ft^2$

Part 3) Hexagon 1: $P=90\ cm$ and $A=\frac{675\sqrt{3}}{2})\ cm^2$

Part 4) Hexagon 2: $P=540\ m$ and $A=12,150\sqrt{3}\ m^2$

Step-by-step explanation:

Part 1) we have an equilateral triangle

we know that

$A=\frac{1}{2}ap$

where

a is the apothem

P is the perimeter

step 1

Find the length side of the equilateral triangle

Let

b ----> the length side of triangle

we know that

The measure of each interior angle is 60 degrees

$tan(30^o)=\frac{4}{b/2}$ ---> by TOA (opposite side divided by the adjacent side)

$tan(30^o)=\frac{1}{\sqrt{3}}$

equate

$\frac{4}{b/2}=\frac{1}{\sqrt{3}}$

$\frac{8}{b}=\frac{1}{\sqrt{3}}$

$b=8\sqrt{3}\ in$

step 2

Find the perimeter

P=3b

$P=3(8\sqrt{3})=24\sqrt{3}\ in$

step 3

Find the area

$A=\frac{1}{2}(4)(24\sqrt{3})=48\sqrt{3}\ in^2$

Part 2) we have a square

we know that

$A=\frac{1}{2}ap$

where

a is the apothem

P is the perimeter

step 1

Find the length side of the square

Let

b ----> the length side of the square

we know that

The diagonal is half the radius of the square

Applying the Pythagorean Theorem

D^2=b^2+b^2

D^2=2b^2

we have

$D=2a=2(10)=20\ ft$

20^2=2b^2

$b^2=200\\b=\sqrt{200}\ ft$

simplify

$b=10\sqrt{2}\ ft$

step 2

Find the perimeter

$P=4b=4(10\sqrt{2})=40\sqrt{2}\ ft$

step 3

Find the area

$A=\frac{1}{2}ap$

The apothem is half the length side of the square

$a=5\sqrt{2}\ ft$

$A=\frac{1}{2}(5\sqrt{2})(40\sqrt{2})$

$A=200\ ft^2$

Part 3) we have a regular hexagon

we know that

$A=\frac{1}{2}ap$

where

a is the apothem

P is the perimeter

step 1

Find the length side of the hexagon

we know that

The length side of a regular hexagon is equal to the radius

Let

b ----> the length side of the hexagon

we have

$b=30/2=15\ cm$ ----> the radius is half the diameter

step 2

Find the perimeter

$P=6b=6(15)=90\ cm$

step 3

Find the area

$A=\frac{1}{2}ap$

The apothem is the height of an equilateral triangle

Applying the Pythagorean Theorem

b^2=(b/2)^2+a^2

15^2=(15/2)^2+a^2

a^2=225-(225/4)

$a^2=675/4\\a=\frac{\sqrt{675}}{2}\ cm$

simplify

$a=\frac{15\sqrt{3}}{2}\ cm$

substitute in the formula of area

$A=\frac{1}{2}(\frac{15\sqrt{3}}{2})(90)$

$A=\frac{675\sqrt{3}}{2})\ cm^2$

Part 4) we have a regular hexagon

we know that

$A=\frac{1}{2}ap$

where

a is the apothem

P is the perimeter

step 1

Let

b ---> the length side of the hexagon

we have

$b=90\ m$

Find the perimeter

$P=6b=6(90)=540\ m$

step 2

Find the area

$A=\frac{1}{2}ap$

The apothem is the height of an equilateral triangle

Applying the Pythagorean Theorem

b^2=(b/2)^2+a^2

90^2=(90/2)^2+a^2

a^2=8,100-2,025

$a^2=6,075\\\\a=\sqrt{6,075}\ m$

simplify

$a=45\sqrt{3}\ m$

substitute in the formula of area

$A=\frac{1}{2}(45\sqrt{3})(540)$

$A=12,150\sqrt{3}\ m^2$

0,0(0 оценок)

Ответ:

strodersage

08.07.2022

Mathematics

3 and 6800

Step-by-step explanation:

0,0(0 оценок)

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.

Ask your question

More tips

C Computers and Internet Step-by-Step Guide on How to Download Music to Your iPhone...
A Animals and plants Unraveling the Mystery of Loch Ness: What Does the Loch Ness Monster Look Like?...
L Leisure and Entertainment Should You Buy a Ceramic Knife?...
C Computers and Internet How to easily and quickly disable Firebug in Gmail and Google Docs...
G Goods and services How to sew a ribbon: Tips for beginners...
F Food and Cooking How to Make Mayonnaise at Home? Secrets of Homemade Mayonnaise...
C Computers and Internet Which Phone is Best for Internet Surfing?...
F Food and Cooking Everything You Need to Know About Pasta...
C Computers and Internet How to Choose a Monitor?...
H Horoscopes, Magic, Divination Where Did Tarot Cards Come From?...

Answers on questions: Mathematics

M Mathematics Marco rode his bike 2 miles in 1/2 of an hour. What was his average speed in miles per hour?...
M Mathematics What is the median of the following data values 98,102,53,80,22...
M Mathematics Ineed to know how to solve 15x - 8 =14x + 13...
M Mathematics Circle r has a radius of 6, and is tangent to circle r at point q. also, qp = 8. (a) what is the measure of angle rqp explain your answer. b) what is the length of rp explain...
M Mathematics Pls i don’t understand and i’m being timed...
M Mathematics Terri is analyzing a circle, y2 + x2 = 36, and a linear function g(x). will they intersect? y2 + x2 = 36 g(x) graph of the function y squared plus x squared equals 36 x g(x)...
M Mathematics Can someone me with algebra? ? will mark and star....
M Mathematics Simplify the square root of 18 completely show all work...
M Mathematics Three or more lines that intersect at a common point...
M Mathematics best answer i will mark as brainliest...

S Sport S Society and Politics G Goods and services C Cities and Countries A Animals and plants L Legal consultation W Work and Career C Construction and repair H Health and Medicine D Dating, Love, Relationships H Horoscopes, Magic, Divination S Style and Beauty L Leisure and Entertainment S Science and Technology P Photography and Videography A Art and Culture O Other P Philosophy F Food and Cooking B Business and Finance T Travel and tourism F Family and Home A Auto and Moto

Full access

It will provide effective and fast learning by providing unlimited access to the knowledge base and receiving answers from experts and an AI advisor.

Ask an AI advisor a question

I want advice

ABOUT US

About us
Terms of use
Copyright
Privacy Policy
Cookie policy
Cookie preferences

HELP

Sign Up
FAQ
Security Center