According to the diagram, which of the following statements about area and perimeter of pentagon abcde is true?
a) area = 25 perimeter = 20
b) area = 30 perimeter = 22.31
c) area = 33 perimeter = 12.5
d) area = 35 perimeter = 18

Option B. Area = 30 Perimeter = 22.31

Step-by-step explanation:

step 1

Find the measure of the sides of the pentagon

Observing the graph

AE= 5 units

ED > Applying Pythagoras theorem

ED²=2²+3²=13

ED=√13 units

DC=3 units

BC=4 units

AB >Applying Pythagoras theorem

AB²=3²+6²=13

AB=√45 units

step 2

Find the perimeter

P=AE+ED+DC+BC+AB

substitute

P=5+√13 +3+4+√45=22.31 units

step 3

Find the area

The area of the figure is equal to the area of two trapezoids

so

A=(1/2)(2+5)(6)+(1/2)(6+3)(2)=21+9=30 units²

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