Question

An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm.
Find the area of the triangle

Answer 1

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

area of a triangle

formula :

$\frac{1}{2} * base * height$

getting the height of the triangle:

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

$c^{2} = a^{2} + b^{2}$

were c is the hypotenuse of 12 cm

a is the adjacent of base (6/2) = 3 cm

and b is the height

$12^{2} = 3^{2} +b^{2}$

$b^{2} = 12^{2} - 3^{2}$

$b^{2} = 135$

$b = \sqrt{135}$

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