The area of the isosceles triangle is `(5)/(4)sqrt11cm^(2)` if the perimeter is `11 cm` and the base is `5 cm.`

Answer

1

Explanation

Let equal sides of an isosceles triangle be `b.`
`therefore"Perimeter of a triangle", " "2s=b+b+5`
`therefore " "11=2b+5`
`rArr " "2b=11-5rArr2b=6`
`rArr " " b=(6)/(2)=3 cm`
We know that, area of an isosceles triangle
`=(a)/(4)sqrt(4b^(2)-a^(2))`
Here, sides of triangle are `a=5 cm` and `b= 3 cm`
`therefore" " "Area of an isosceles triangle"=(5sqrt(4(3)^(2)-(5)^(2)))/(4)`
`=(5sqrt(4xx9-25))/(4)`
`=5sqrt((36-25))/(4)`
`=5sqrt(11)/(4)cm^(2)`