Find the area of the regular polygon,2√3 and 5

Answer

Correct option is

D

5 cm

△ABC is an equilateral △

∴Area=  

4

3

​  

​  

a  

2

=75  

3

​  

⟹ a  

2

=300

a=10  

3

​  

cm

AM=MC=  

2

10  

3

​  

​  

=5  

3

​  

cm

Area =  

2

1

​  

×AC×BM

75  

3

​  

=  

2

1

​  

×10  

3

​  

×BM  

∴BM=15cm

△AOC,△BOC and △AOB are of equal area

∴ar(△AOC)=  

3

1

​  

ar(△ABC)=  

3

1

​  

×75  

3

​  

=25  

3

​  

cm  

2

In △AOC,

ar(△AOC)=  

2

1

​  

×AC×OM

⇒25  

3

​  

=  

2

1

​  

×10  

3

​  

×OM  

∴OM=5cm Ans.

answer with step-by-step explanation:

a. ∠j is supplementary to ∠k - true:

(opposite angles of a trapezoid are supplementary which means that they add up to 180 degrees)

b. kl is parallel to jm - true:

(opposite sides are parallel to each other in a trapezoid)

c. jk is perpendicular to kl - false:

(clearly, jk does not make a right angle with kl)

d. jk is parallel to lm - false:

(jk and lm are two lines opposite in direction to each other so they cannot be parallel)

e. ∠j is congruent to ∠m - true:

(the angles on each side of the base are congruent)

f. ∠j is congruent to ∠k - false:

(the angles on the same side but opposite side of the base are not congruent)