Question

Use π = 3.14. Determine the area and perimeter of the figures below. (Use π = 3.14. Round your answers to two decimal places.)
(a) Assume that a = 8 m.

Answer 1

@DelTaVsPi

Answer 2

okay, let me have a look at this :)

Answer 3

thanks

Answer 4

Okay, so this image is composed of two smaller shapes, a semi-circle and a triangle :)

Answer 5

So lets solve the area first :) Because I like area questions haha XD

Answer 6

it sure is

Answer 7

lets do it

Answer 8

I'm going to split this into two separate areas, like for example Area 1 and Area 2

Answer 9

First we are going to solve for the semi circle first :)

Answer 10

now, like always, we need to interpret carefully about the shape ! The semi-circle is composed of 180 degrees since it is half a circle

Answer 11

Thus the formula is \[A = \frac{ \theta }{ 360 }\times \pi \times r^2\]

Answer 12

Since "8" is the diameter --> the radius is half of 8, so it is 4.
now 180/360 = 1/2

Sooo...
A = 1/2 x Pi x (4)
= 25.1327 Units^2

Answer 13

So this will be Area 1

Answer 14

Now we can solve for Area 2

Answer 15

awesome!

Answer 16

The area of the triangle is\[A = \frac{ 1 }{ 2 }\times Length \times height\]

Answer 17

A = 1/2 x 8 x 8
= 32 units squared

Answer 18

Okay the "Total Area"
is given by
A = Area 1 + Area 2
= 25.1327 + 32
= 57.1327 Units squared

Answer 19

Okay cool, so now Area is completed, how do you feel about it?

Answer 20

so is that area all togethers answer?

Answer 21

Yeap that sounds about right!

Answer 22

We can move onto findign the perimeter, once you are ready

Answer 23

it says thats wrong

Answer 24

Hmmm... let me check

Answer 25

okay

Answer 26

Hmm.. I'm not entirely sure where I could have gone wrong for the Area.

Answer 27

We could move onto solving the Perimeter, we can get back to find the area later :)

Answer 28

okay sounds good

Answer 29

The perimeter of a semicircle is given by \[P = \frac{ 1 }{ 2 }\times 2\pi \times r\]

Answer 30

r = 4
So -> P = 1/2 x 2(Pi) x (4)
= 12.566 Units

Answer 31

This will be perimeter 1

Answer 32

Now we can solve for Perimeter 2