All categories

3 years ago

A regular octagonal pyramid. Each side of the base is 6 cm long. it has a height of 10cm. Find the surface area of the pyramid

Mathematics

2 answers:

attashe74 [19]3 years ago

8 0

9514 1404 393

Answer:

470.16 cm²

Step-by-step explanation:

The apothem of the base is used for two purposes: to find the area of the base, and to find the slant height of each face.

The apothem of the base for side length s is ...

s/2 = a·tan(π/8)

a = s/(2·tan(π/8)) ≈ 7.24 cm

The slant height of a triangular face is found using the Pythagorean theorem. The apothem of the base and the height are legs of the right triangle whose hypotenuse is the slant height. For slant height x, we have ...

x² = 10² + a² = 100 +52.46

x ≈ √152.46 ≈ 12.35

The area of the 8 triangular faces will be ...

A = 1/2Px . . . . where P is the perimeter of the pyramid

The area of the base will be ...

A = 1/2Pa

So, the total surface area is ...

A = 1/2P(a + x) = (1/2)(8)(6 cm)(7.24 +12.35 cm) ≈ 470.16 cm²

nata0808 [166]3 years ago

8 0

The answer is 470.16 cm²

You might be interested in

Solve to get the value of h

iragen [17]

The answer to the question is h=64 degrees

4 0

3 years ago

Read 2 more answers

Can someone help me I need the answers to 1-4 ty!!

lubasha [3.4K]

1. x=-3 y=4 2. x=5/2 y=15/2 3. x=9/5 y=-36/5 4. x=-2 y=1

8 0

3 years ago

Simple Interest on £50 at 3% for 2 years

Semenov [28]

Answer:l

Step-by-step explanation:L

6 0

3 years ago

On a coordinate plane, a line has points (negative 2, negative 4) and (4, 2). Point P is at (0, 4). Which points lie on the line

NikAS [45]

Answer:

the correct options are:

(–1, 3), (–2, 2) and (–5, –1)

Step-by-step explanation:

Given that a line passes through two points

A(-2, -4) and B(4, 2)

Another point P(0, 4)

To find:

Which points lie on the line that passes through P and is parallel to line AB ?

Solution:

First of all, let us the find the equation of the line which is parallel to AB and passes through point P.

Parallel lines have the same slope.

Slope of a line is given as:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{2-(-4)}{4-(-2)} = 1$

Now, using slope intercept form ( $y = mx+c$ ) of a line, we can write the equation of line parallel to AB:

$y =(1)x+c \Rightarrow y = x+c$

Now, putting the point P(0,4) to find c:

$4 = 0 +c \Rightarrow c = 4$

So, the equation is $\bold{y=x+4}$

So, the coordinates given in the options which have value of y coordinate equal to 4 greater than x coordinate will be true.

So, the correct options are:

(–1, 3), (–2, 2) and (–5, –1)

8 0

3 years ago

Read 2 more answers

160 is 120% of what number?

LuckyWell [14K]

120 % = 160

---------------------------------------------------------------------------
Find 1 % :
---------------------------------------------------------------------------
120% = 160
1% = 160 ÷ 120
1% = 4/3

---------------------------------------------------------------------------
Find 100% :
---------------------------------------------------------------------------
1% = 4/3
100% = 4/3 x 100
100% = 133 1/3

---------------------------------------------------------------------------
Answer: 160 is 120% of 133 1/3
---------------------------------------------------------------------------

8 0

3 years ago

Read 2 more answers

A regular octagonal pyramid. Each side of the base is 6 cm long. it has a height of 10cm. Find the surface area of the pyramid​

A regular octagonal pyramid. Each side of the base is 6 cm long. it has a height of 10cm. Find the surface area of the pyramid