Answer:
the area of the triangle is 17.4cm^2
Step-by-step explanation:
Finding the area of a triangle
an isosceles triangle has two sides of equal length.
therefore to get the base of the triangle :
we need to subtract the lengths from he perimeter
30-12-12
= 6
the base of the triangle is 6 cm
formula :
[tex]\frac{1}{2} * base * height\\[/tex]
we make use of one side of the triangle , half the base. this creates a right angled triangle
we can make use of the formula
[tex]c^{2} = a^{2} + b^{2}[/tex]
were c is the hypotenuse of 12 cm
a is the adjacent of base (6/2) = 3 cm
and b is the height
[tex]12^{2} = 3^{2} +b^{2}[/tex]
[tex]b^{2} = 12^{2} - 3^{2}[/tex]
[tex]b^{2} = 135\\[/tex]
[tex]b = \sqrt{135}[/tex]
b = 11.6 cm to 3sf
the height is 11.6cm.
area of the triangle is :
1/2 * 3 * 11.6
= 17.4 cm^2
the area of the triangle is 17.4cm^2