Best Answer

The area is about 695.29 square units.

A = 2(1 + sqrt2)S2 where S is a side length

P = 8*S

S = 12

A = (2 + 2 sqrt2) 144

A = 288 + 288 sqrt2

A = 288 + 407.29

A = 695.29

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Derivation

The area of a regular polygon is:

Area = (1/2)(p)(a), where p is the perimeter and a the apothem.

Since we know the perimeter, and also the length of each side of our octagon which is 12 (96/8), we need to find the length of the apothem a.

Let's take a look at one of the right triangle which is formed when we draw the radius from the center to one of the vertices, and the apothem a from the center perpendicular to the side s.

In this right triangle we have:

side s = 6 (12/2)

angle opposite to apothem = 67.5 degrees (135/2)

So that,

tan 67.5 degrees = a/s

a = (tan 67.5 degrees)(6)

a = 14.5 (approximately)

Thus,

Area = (1/2)(p)(a)

Area = (1/2)(96)(14.5)

Area = 696

Q: What is the area of a regular octagon with a perimeter of 96?

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What are the dimensions of a rectangle that has a perimeter of 56 units and an area of 96 square units

4 x 24

Assuming 96 refers to the area of therectangle, the answer is: infinite. Consider the following sequence of rectangles with breadh B units and length L units.: Breadth = 1 Length = 96. Area = 96, Perimeter = 194 B= 0.1, L = 960. A = 96, P = 1920.2 B = 0.01, L =9600. A = 96, P = 19200.02 B = 0.001, L = 96000. A = 96, P = 192000.002 There is no limit to how small B can get and therefore, how large P can get.

Perimeter is total edge length. A stop sign has 8 sides, so 8"*12=96"■

Perimeter = 12+12+12+12 = 48

Related questions

12ft

The perimeter is 8 times 12 = 96 inches

Length + width = 18 cm so length = 12 cm and width = 6 cm. Presumably the length is the common side so the perimeter of the octagon is 8 x 12 = 96 cm. If the width is the common side then the perimeter of the octagon is 8 x 6 = 48 cm

we make the assumption that all sides are equal length, that is to say it is a regular octagon. Then one side has length 12 if 2 sides have length 23. So the perimeter is 8x12=96 cm

Octagon: 8 sides; each side 12 cm; 12 x 8 = 96 cm

The area is 96*sqrt(3) = 166.3 sq inches, approx.

44499 sq ft (approx)

96 feet.

What are the dimensions of a rectangle that has a perimeter of 56 units and an area of 96 square units

An octogon has eight sides. The perimeter is the distance around the outside edge. The perimeter is therefore 12" x 8 = 96". Since 12" = 1', you could also described the perimeter as being 8'.

4X24

The perimeter of the square is 96.