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2 years 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]2 years 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]2 years 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

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What does a proportion look like?

AURORKA [14]

A proportion looks like this:

$a\div b = c\div d$

It means that the quantity a,b,c and d are in the same proportion: the ratio between a and b is the same ratio between c and d.

They are particularly useful in situation when you have an example given, and you want to extrapolate the relationship for another couple.

For example, you can think of the following problem: "Five apples cost 2 dollars. How much will 8 apples cost?"

You can build the proportion

$5\div 2 = 8\div x$

And then solve it for x:

$\dfrac{5}{2}=\dfrac{8}{x} \iff 5x=16 \iff x = \dfrac{16}{5} = 3.2$

6 0

3 years ago

The scores on a test for a sample of 42 statistics students are summarized in the following table. 9, 90, 18, 80, 15, 70. Find t

igomit [66]

<h3>Answer: 78.6</h3>

Work Shown:

$\begin{array}{|c|c|} \cline{1-2}\text{Number of People} & \text{Score}\\\cline{1-2}9 & 90\\\cline{1-2}18 & 80\\\cline{1-2}15 & 70\\\cline{1-2}\end{array}$

Multiply across the rows to form a third column. Example: 9*90 = 810 in the first row.

$\begin{array}{|c|c|c|} \cline{1-3}\text{Number of People} & \text{Score} & \text{Number*Score}\\\cline{1-3}9 & 90 & 810\\\cline{1-3}18 & 80 & 1440\\\cline{1-3}15 & 70 & 1050\\\cline{1-3}\end{array}$

The values in the third column add to 810+1440+1050 = 3300

Divide this over the total number of people which is 9+18+15 = 42

The mean is 3300/42 =78.571 approximately which rounds to 78.6

5 0

2 years ago

Aubrey claims that if the dimensions of the parallelogram shown are doubled, then the area of the larger parallelogram will be 4

Ostrovityanka [42]

Answer:

Aubrey is correct because the area of the new parallelogram is 12 (6) = 72 square inches. The original area is 18 square inches. Since 4 (18) = 72, the new parallelogram has 4 times the area of the original.

Step-by-step explanation:

A parallelogram with a base of 6 inches and height of 3 inches. A side has a length of 5 inches.

Aubrey is correct because the area of the new parallelogram is 10 (7) = 70 square inches. The original area is 18 square inches. Since 4 (18) = 72, it is about 4 times larger than the original.

Aubrey is incorrect because if one doubles each dimension, then the area will automatically be doubled as well. The original area is 18 square inches so the new parallelogram will have an area of 2 (18) = 36, or two times more than the original.

Aubrey is incorrect because if one doubles each dimension, then the area will automatically be doubled as well. The original area is 30 square inches so the new parallelogram will have an area of 2 (30) = 60, or 2 times more than the original.

Workings

Area of a parallelogram=base×height

Original parallelogram

Base=6 inches

Height=3 inches

Area=base×height

=6×3

=18 square inches

New parallelogram with doubled dimensions

Base=6 inches doubled=12 inches

Height=3 inches doubled=6 inches

Area=base×height

=12×6

=72 square inches

New area=4 times original area

New area=4×18

New area=72 square inches

5 0

3 years ago

Help pls also show work if needed!

neonofarm [45]

Answer AND Step-by-step explanation:

Everything is in the picture.

#teamtrees #PAW (Plant And Water)

The equation is:

$c = -\frac{1}{2} t + 6$

5 0

3 years ago

Which two expressions are

Oxana [17]

Answer:

9(2p-18) and 2(9p-18)

Step-by-step explanation:

6 0

3 years ago