Answer :
the height of triangle is 6cm
then base length is found by pythagoras theorem
[tex] a^{2}= ( \frac{a}{2} )^{2}+ h^{2} [/tex]
[tex] \frac{3a^2}{4}=36 [/tex]
[tex] a^{2}=48 [/tex]
[tex]a= \sqrt{48} [/tex]
The area of the triangle
[tex]= \frac{1}{2}ah =3 \sqrt{48}=20.7846 cm^2 [/tex]
then base length is found by pythagoras theorem
[tex] a^{2}= ( \frac{a}{2} )^{2}+ h^{2} [/tex]
[tex] \frac{3a^2}{4}=36 [/tex]
[tex] a^{2}=48 [/tex]
[tex]a= \sqrt{48} [/tex]
The area of the triangle
[tex]= \frac{1}{2}ah =3 \sqrt{48}=20.7846 cm^2 [/tex]
Height of equilateral triangle is √3/2 X a, where 'a' is the side of the equilateral triangle. So √3/2 x a = 6.
Hence a = 12/√3.
Area of an equilateral triangle is 1/2 base x height
ie 1/2 x 12 ÷ √3 x 6 = 36 ÷√3
= 12√3.
Hence a = 12/√3.
Area of an equilateral triangle is 1/2 base x height
ie 1/2 x 12 ÷ √3 x 6 = 36 ÷√3
= 12√3.