Mathematics, 16.04.2020 19:21 mariam00000w

A stop sign is a regular octagon. The standard stop sign has a 16.2 inch radius. The area of a standard stop sign is
square inches. Please round your answer to the nearest whole number

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The area of standard stop sign regular octagon is 742.3 squared inches, if the standard stop sign has a 16.2 inch radius.

Step-by-step explanation:

The given is,

Radius of standard stop sign is 16.2 inch radius

Step:1

The regular octagon is equal to the 16 right angled triangle,

Angle of right angle triangle = $\frac{360}{16}$ = 22.5°

Ref attachment,

From the OAB right angle triangle,

Trigonometric ratio,

sin ∅ = $\frac{Opp}{Hyp}$

Where, ∅ = 22.5°

Hyp = Radius = 16.2 inches

Ratio becomes,

sin 22.5°= $\frac{b}{16.2}$

b = (0.374607)(16.2)

b = 6.19947 inches

Trigonometric ratio,

cos ∅ = $\frac{Adj}{Hyp}$

Where, ∅ = 22.5°

Hyp = Radius = 16.2 inches

Adj = h

Ratio becomes,

cos 22.5°= $\frac{h}{16.2}$

h = (0.9238795)(16.2)

h = 14.967 inches

Step:2

From the triangle OAC,

Area, $A = \frac{1}{2} (Height )( Base)$

Where, Height = 14.967 inches

Base = b + x = 6.19947 + 6.19947

= 12.3989 inches

From the values equation becomes,

A = $\frac{1}{2} (14.967)(12.39894)$

A = 92.7875 Squared inches

Step:3

The octagon is equal to sum of 8 triangles

Area of octagon = 8 × Area of triangle

= 8 × 92.7875

= 742.3 squared inches

Result:

The area of standard stop sign regular octagon is 742.3 squared inches, if the standard stop sign has a 16.2 inch radius.

A stop sign is a regular octagon. The standard stop sign has a 16.2 inch radius. The area of a stand

Answer from: Quest

3432532

step-by-step explanation:

Answer from: Quest

the answer to the expression is 83

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A stop sign is a regular octagon. The standard stop sign has a 16.2 inch radius. The area of a stand...