An isosceles triangle have two congruent sides
The total height of the star is 14.12 cm
From the question, we have the following parameters
[tex]\mathbf{Base = 4.2}[/tex]
[tex]\mathbf{Length = 6}[/tex]
The height of one isosceles triangle, can be calculated using Pythagoras theorem.
[tex]\mathbf{a^2 = b^2 + c^2}[/tex]
Where:
[tex]\mathbf{b = \frac{Base}{2}=\frac{4.2}{2}= 2.1}[/tex]
[tex]\mathbf{c = height}[/tex]
[tex]\mathbf{a = Length = 6}[/tex]
So, we have:
[tex]\mathbf{6^2 = 2.1^2 + c^2}[/tex]
Collect like terms
[tex]\mathbf{c^2 = 6^2 - 2.1^2}[/tex]
[tex]\mathbf{c^2 = 31.59}[/tex]
Take square roots
[tex]\mathbf{c = 5.62}[/tex]
The height (h) of the star is:
[tex]\mathbf{h = 8.5 + 5.62}[/tex]
[tex]\mathbf{h = 14.12}[/tex]
Hence, the total height of the star is 14.12 cm
Read more about isosceles triangles at:
https://brainly.com/question/16719933
