Find the perimeter and area of the regular polygon. Round answers to the nearest tenth.

Mathematics

1 answer:

e-lub [12.9K]3 years ago

6 0

Answer: Perimeter = 72.67

Area = 363.3

Step-by-step explanation:

The given polygon is a pentagon. The apotherm is the perpendicular line from the midpoint of the Pentagon to the base of one of its sides.

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

Area = a² × n × tan 180/n

Where n represents the number of sides of the polygon.

n = 5

Apotherm = 10

Therefore,

Area = 10² × 5 × tan(180/5)

Area = 500 × tan 36

Area = 363.3

The formula for determining the perimeter of a regular polygon is

P = 2 × area/apotherm

Perimeter = 2 × 363.3/10

Perimeter = 72.67

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Let A and B be sets with cardinal numbers , n(A) = a and n(B) = b respectively . Decide whether the statement is true or false.

olya-2409 [2.1K]

Answer:

True

Step-by-step explanation:

$A\cup B=A\cup(A-B)\\\\A\ and\ A-B\ are\ disjoint\ that\ means\ there\ is\ no\ common\ element\ in\ these\ two.\\\\n(A\cup B)=n(B\cup(A-B))\\\\n(A\cup B)=n(B)+n(A-B)\ \ \ \ \ \ \ as\ for\ disjoint\ set\ P,Q\ n(P\cup Q)=n(P)+n(Q)\\\\(n(P-Q)=n(P)-n(P\cap Q))\\\\n(AUB)=n(B)+n(A-B)\\\\n(AUB)=n(B)+n(A)-n(A\cap B)\\\\n(AUB)=n(A)+n(B)-n(A\cap B)\\\\Hence\ given\ statement\ is\ true$