All categories

3 years ago

Find the area of a regular octagon with an apothem of 8

Mathematics

1 answer:

xenn [34]3 years ago

6 0

Answer:

308cm²

Step-by-step explanation:

Assuming the given unit is in cm

The expression for the area of a regular Octagon is

A=2(1+√2)a²

Given the apothem a = 8cm

Substituting we have

A=2(1+√2)8²

A= 2(1+1.414)64

A= 2(2.414)64

A= 308cm²

You might be interested in

Finding the Slope of a Line from a Table

lakkis [162]

Answer:

m = rise / run = 1/7

Step-by-step explanation:

Recall that the slope of a line is m = rise / run.

Here we look at x first (to calculate the run): x begins at -7 and ends at 0. Thus, the run is 0 - (-7), or 7.

Now look at how y behaves (find the rise): y begins at 0 and ends at 1. Thus, the rise is 1.

Therefore the slope of the line connecting the two poings given is

m = rise / run = 1/7

3 0

3 years ago

Whats number 7?? im so confused!!

I am Lyosha [343]

Maybe D? I'm not exactly sure, I'm sorry

7 0

3 years ago

The width of a box in the shape of a rectangular prism is 4 inches more than the height h . The length is the difference of 9 in

Doss [256]

Answer:

$(a)$ $V = -H^3+ 5H^2 + 36H$

$(b)$ $Length = 5in; Width = 9in; Height = 5in$ or $Length = 3in; Width = 10in; Height = 6in$

Step-by-step explanation:

Let:

$W=Width; L = Length; H = Height$

Given

$W = 4 + H$

$L = 9 - H$

Solving (a): The polynomial for the volume in terms of height

Volume (V) is calculated using:

$V = L * W * H$

$V = (9 - H) * (4 + H) * H$

Expand

$V = (9 - H) * (4H + H^2)$

Open brackets

$V = 36H + 9H^2 - 4H^2 - H^3$

$V = 36H + 5H^2 - H^3$

Rewrite as:

$V = -H^3+ 5H^2 + 36H$

Solving (b): The dimensions when Volume = 180

Substitute 180 for V in: $V = -H^3+ 5H^2 + 36H$

$180 = -H^3+ 5H^2 + 36H$

Rewrite as:

$H^3 - 5H^2 - 36H + 180 = 0$

Factorize:

$H^2(H - 5) - 36(H - 5) = 0$

$(H^2 - 36)(H - 5) = 0$

Express $H^2 - 36$ as difference of two squares

$(H - 6)(H + 6)(H - 5) =0$

This gives:

$H - 6 =0==> H = 6$

$H + 6 =0==> H = -6$

$H - 5 =0==> H = 5$

Since the height can not be negative, then H = 5 or H = 6

Recall that:

$W = 4 + H$

$L = 9 - H$

When H = 5

$W = 4 + 5 = 9$

$L = 9 - 5 = 4$

When H = 6

$W = 4 + 6 = 10$

$L = 9 - 6 = 3$

Hence, the dimensions of the box are:

$Length = 5in; Width = 9in; Height = 5in$

$Length = 3in; Width = 10in; Height = 6in$

3 0

3 years ago

Kirsten and Molly are on a 3-day bike ride. The entire route is 156 miles. On the first day they biked 64 miles, and on the seco

timama [110]

The distance that Kirsten and Molly need to bike on their third day is obtained by subtracting the sum of the distances they have traveled after two days from the length of the entire route.

distance left = 156 miles - (64 miles + 45 miles)
= 47 miles
Thus, Kirsten and Molly need to bike 47 miles on their third day.

3 0

3 years ago

What is the ratio for 4, 8, 12, 14 (r)

olasank [31]

answer for this question is 2 is to 4 is to6 is to 7

7 0

2 years ago