Question

if the perimeter of an equilateral triangle is 36cm, calculate its area and height ​

Answer 1

Answer:

Your answer is H = 6√3 ; Area = 36√3

Step-by-step explanation:

Given :

perimeter = 36cm

to find :

Height and area

Solution:

method I:

Here H is CD

Let us take the triangle CDB

sin B = Opp / hyp

sin60 = H / 12        (in equilateral triangle the angles will be 60 degree )

√3/2 = H/12

6√3cm = H

Area of the Δ ABC were S = 12cm H = 6√3cm

= 1/2(S)(H)

=1/2(12)(6√3)

= (6)(6√3)

= 36√3 cm²

Your answer is H = 6√3 ; Area = 36√3

method II:

Here H is CD

Let us take the triangle CDB

And DB as 12/2 = 6m

By Pythagoras theorem :

H² + 6² = 12²

= H² = 144 - 36

= H = √108

= H =√36(3)

= H = 6√3

Area of the Δ ABC were S = 12cm H = 6√3cm

= 1/2(S)(H)

=1/2(12)(6√3)

= (6)(6√3)

= 36√3 cm²

Your answer is H = 6√3 ; Area = 36√3

Hope this helps u a lot

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Diagram of the triangle given below: