Math, asked by adityachangedia07, 4 months ago


9. ABCD is a square. E is a point as shown in figure such that ADCE is equilateral.
Area of ADCE = 16UNDERROOT3 units. Find area of square ABCD​

Answers

Answered by Anonymous
3

Answer:

⇒ Side of a square, ABCD=4cm

It is given that △CED is an equilateral triangle.

∴ EC=CD=DE=4cm

⇒ ∠ECD=60

o

. [ An angle of an equilateral triangle ]

AC is a diagonal of a square ABCD

∴ ∠ACD=45

o

.

⇒ ∠ECA=∠ECD−∠ACD

⇒ ∠ECA=60

o

−45

o

⇒ ∠ECA=15

o

In △ACE, draw perpendicular EM the base AC.

Now in △EMC,

⇒ sin15

o

=

H

P

=

EC

EM

⇒ sin15

o

=

4

EM

2

2

(

3

−1)

=

4

EM

⇒ (

3

−1)×

(2

2

×

2

)

2

=

4

EM

[ By rationalizing the denominator ]

4

2

(

3

−1)

=

4

EM

⇒ EM=

2

(

3

−1)

Diagonal of a square, (AC)=

2

a

AC=

2

×4=4

2

Diagonal of a square =4

2

cm

Now, in △AEC,

⇒ Area of △AEC=

2

1

×AC×EM

=

2

1

×4

2

×

2

(

3

−1)

=4(

3

−1)cm

2

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