Question

Find area of isosceles triangle whose base is 6 cm and erimeter is 16 cm

Answer 1

in an isosceles triangle,
any two sides are equal

let each of the equal side be x
perimeter=16cm
base=6cm

therefore,
x+x+6=16
2x=16-6
2x=10
x = \frac{10}{2}x=210​ 
x=5

area of triangle =½×base×height

since we need the height,
we draw a perpendicular from the base which will divide this triangle into two right angled triangles 
with each base = to 6/2=3cm
hypotenuse is the side of isosceles triangle which is 5cm
let the height be x


Using Pythagoras theorem,
we have,

{3}^{2} + {h}^{2} = {5}^{2}32+h2=52 
9 + {h}^{2} = 259+h2=25 
{h}^{2} = 25 - 9h2=25−9 
{h}^{2} = 16h2=16 
h = \sqrt{16}h=16​ 
h=4
height is 4cm

area of triangle= ½×base×height
= \frac{1}{2} \times 6 \times 4=21​×6×4 
= 12 {cm}^{2}=12cm2 
is the area

Answer 2

of isosceles triangle=2height+base
=(2*x)+6=16
2x=16-6
2x=10
x=5

height =5cm

area of isosceles triangle=(base*height)/2
$\frac{5 \times 6}{2}$
$= 5 \times 3 = 15c {m}^{2}$