All categories

1 year ago

Find the area of a regular octagon with an apothem length of 10 and a side length of 6.

Mathematics

2 answers:

Sauron [17]1 year ago

8 0

Answer:

A = 240 units²

Step-by-step explanation:

the area (A) of a regular polygon is

A = $\frac{1}{2}$ pa ( p is the perimeter and a the apothem )

here p = 8 × 6 = 48 ( an octagon has 8 sides ) and a = 10 , then

A = $\frac{1}{2}$ × 48 × 10 = 24 × 10 = 240 units²

ruslelena [56]1 year ago

6 0

Answer:

Step-by-step explanation:

Preliminary task

Draw a regular octagon.

Draw a perpendicular from the side's midpoint to the center. (That is the apothem).

Draw two radii from the center of the side to the center of of the octagon. The endpoints of these two radii is the endpoints of the octagon's side.

The octagon has 8 such triangles.

Area one triangle

Area = 1/2 * side * apothem

side = 6

apothem = 10

Area = 1/2 6 * 10

Area = 30

Area of 8 such triangles.

Area = 8 * area of 1 triangle

area 1 triangle = 30

Area of 8 such triangles = 30*8 = 240

Answer 240

You might be interested in

Simplify the expression (3 - 4i)(1 + 5i) - (2 - i). Show your work please! I have the answer: 21 + `12i but I need to show my wo

masha68 [24]

Answer:

21+12i i hope this will help you

Step-by-step explanation:

(3-4i)(1+5i)-(2-i)

=[3(1+5i)-4i(1+5i)]-(2-i)

=[3+15i-4i-20i²]-(2-i)

=(3+11i-20i²)-(2-i)

opening brackeys

=3+11i-20i²-2+i

=3+11i+1i-20i²-2

as we know that i²=-1

=3-20(-1)-2+12i

=3+20-2+12i

=21+12i

8 0

2 years ago

Danielle worked at the warehouse after school. She earned $9.25 per

Elza [17]

Huh? I honestly am lost in this world it’s draining my mental health....what if I just end it? Will anyone care? Probably not....... I’m not allowed to feel this way bc my parents say it’s the devil trying to take me away from god but honestly I don’t believe that..

6 0

2 years ago

If an arithmetic progression satisfies U4=7 , U8=15 .Find U10

Alja [10]

Answer:

U10 = 19

Step-by-step explanation:

The sequence is $Ux=(x*2)-1$

x is the coefficient to U.

So, $U10=(10*2)-1$

Which means $U10=20-1$

Which means $U10=19$

And there is your answer.

Hope this helps. Have a nice day.

6 0

2 years ago

The power generated by an electrical circuit (in watts) as function of its current x (in amperes) is modeled by: P(x)=-12x^2 +12

Minchanka [31]

Given:

The power generated by an electrical circuit (in watts) as function of its current x (in amperes) is modeled by:

$P(x)=-12x^2+120x$

To find:

The current that will produce the maximum power.

Solution:

We have,

$P(x)=-12x^2+120x$

Here, leading coefficient is negative. So, it is a downward parabola.

Vertex of a downward parabola is the point of maxima.

If a parabola is $f(x)=ax^2+bx+c$ , then

$Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)$

In the given function, a=-12 and b=120. So,

$-\dfrac{b}{2a}=-\dfrac{120}{2(-12)}$

$-\dfrac{b}{2a}=-\dfrac{120}{-24}$

$-\dfrac{b}{2a}=5$

Putting x=5 in the given function, we get

$P(5)=-12(5)^2+120(5)$

$P(5)=-12(25)+600$

$P(5)=-300+600$

$P(5)=300$

Therefore, 5 watt current will produce the maximum power of 300 amperes.

6 0

2 years ago

There are 4 sticks, you pick up one stick. How many sticks are left

LenaWriter [7]

There are 3 sticks because:

4 sticks is the total and when you take away 1 stick, it is

4 - 1, which equals 3 sticks

So, the answer is 3 sticks are left.

Question: If u are in high school, why did you ask this question? You already know 4-1=3. Im guessing it was either a joke, or u were helping other people get points. If it is the second one, thx!!

6 0

2 years ago

Read 2 more answers