Express sin F as a fraction in simplest terms. D 17 10 E F
1 answer:
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Answer:
Part a) The slant height is
Part b) The lateral area is equal to
Step-by-step explanation:
we know that
The lateral area of a right pyramid with a regular hexagon base is equal to the area of its six triangular faces
so
where
b is the length side of the hexagon
l is the slant height of the pyramid
Part a) Find the slant height l
Applying the Pythagoras Theorem
where
h is the height of the pyramid
a is the apothem
we have
substitute
Part b) Find the lateral area
we have
substitute the values
the complete question in the attached figure
we know that
r=3 in
A=π*r²
the area of the complete circle-------> π*3²=9π in²
the green sector=360°-75°=285°
if 9π in²--------------------------> corresponds a 360°
X---------------------------------> 285°
X=285*9π/360=(285/40)*π---> [(3*5*19)/(8.5)]*π=[(3*19)/(8)]*π=(57/8)*π in²
the answer is (57/8)*π in² (the option B)
we know that
r=3 in
A=π*r²
the area of the complete circle-------> π*3²=9π in²
the green sector=360°-75°=285°
if 9π in²--------------------------> corresponds a 360°
X---------------------------------> 285°
X=285*9π/360=(285/40)*π---> [(3*5*19)/(8.5)]*π=[(3*19)/(8)]*π=(57/8)*π in²
the answer is (57/8)*π in² (the option B)