Write the quadratic equation in standard form.
2 answers:
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Method 1: In order to find out the area of an octagon with a radius of 4 feet, we have to split the whole figure into 8 equal isosceles triangles.
Therefore,
We will find out the area of one triangle and multiply the area with 8 to, figure out the area of the whole octagon there are 8 similar triangles and all of them will have the same area.
Method 2: From method 1, it would take time as there are too much of calculation, therefore we would go for the shortcut using the formula:
Area = 2√2 × r²
where r<span> is the radius of the octagon.
Substituting the values,
We get:
</span>Area = 2√2 × 4²
Area = 2√2 × 16
Area = 2× 1.41 × 16
Area = 2.828 × 16
Area = 45.25
Rounded to the nearest tenth:
Area = 45.3 ft²
Therefore,
We will find out the area of one triangle and multiply the area with 8 to, figure out the area of the whole octagon there are 8 similar triangles and all of them will have the same area.
Method 2: From method 1, it would take time as there are too much of calculation, therefore we would go for the shortcut using the formula:
Area = 2√2 × r²
where r<span> is the radius of the octagon.
Substituting the values,
We get:
</span>Area = 2√2 × 4²
Area = 2√2 × 16
Area = 2× 1.41 × 16
Area = 2.828 × 16
Area = 45.25
Rounded to the nearest tenth:
Area = 45.3 ft²
Answer:
AKPOS/ACGF = 28√3 -48 ≈ 0.497423
Step-by-step explanation:
Let's assume the square is a unit square. Then the height of the triangle is ...
1 +(√3)/2 = h
and half the base of the triangle is ...
h/√3 = (√3)/3 +1/2 = b/2
The area of the triangle is the product of these:
A = (1/2)bh
= (2 +√3)/2 × (3 +2√3)/6
= (6 +3√3 +4√3 +6)/12 = (12 +7√3)/12
So, the ratio of the area of the square to that of the triangle is the inverse of this, or ...
(square area)/(triangle area) = 12/(12+7√3)
(square area)/(triangle area) = 28√3 -48
