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2 years ago

Find the area of the polygon

Mathematics

1 answer:

Helen [10]2 years ago

8 0

Answer:

Step-by-step explanation:

Assuming a perpendicular line(apotherm) is extended from the midpoint of the polygon to the midpoint of one of its sides, then we can determine the length of the apotherm by applying Pythagorean theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Let a represent the apotherm

Hypotenuse = 4

Apotherm = a

Opposite = a(apotherm = length of each side/2)

Therefore,

4² = a² + a²

16 = 2a²

a² = 16/2 = 8

a = √8 = 2√2

The formula for determining the area of a polygon is expressed as

Area = a² × n × tan 180/n

Where n represents the number of sides of the polygon.

n = 6

Therefore,

Area = (2√2)² × 6 × tan(180/6)

Area = 48 × tan 30

Area = 27.2

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kondaur [170]

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2 years ago

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yulyashka [42]

Answer:

x= -3/2

Step-by-step explanation:

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2 years ago

Prove the polynomial identity.

Kaylis [27]

Answer:

Proven

Step-by-step explanation:

We prove the polynomial with factorization. We must first simplify the expression before we can factorize:

$(4\cdot{x^2}-2)\cdot{(4\cdot{x^2}-2)}-16\cdot{x^4}$

$16\cdot{x^4}-8\cdot{x^2}-8\cdot{x^2}+4-16\cdot{x^4}$

$4-16\cdot{x^2}$

4 is the common number and we can take it out of the expression:

$4\cdot{(1-4\cdot{x^2})}$

We can factorize further with the x term being zero. For this to be true we must have -2x and 2x to cancel out and therefore the expression is proven:

$4\cdot{(1-2\cdot{x})}\cdot{(1+2\cdot{x})}$