Question

find the area of an isosceles triangle whose equal sides are 12 cm each and the perimeter is 30 cm.

Answer 1

Length of first side of triangle =a=12 cm

Length of second side of triangle =b=12 cm

Perimeter of triangle =30 cm

Length of third side of triangle =c=Perimeter of triangle-a-b=30−12−12=6 cm

Semi-perimeter of triangle =s=a+b+c2=12+12+62=15 cm

Using Heron's formula to find area of triangle, we get

Area of triangle =s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√=15(15−12)(15−12)(15−6)−−−−−−−−−−−−−−−−−−−−−−−√

=15×3×3×9−−−−−−−−−−−
answer is 9√15 cm2
as √15 is 3.873 cm
then 9×3.873=34.85

Answer 2

According to given sum,

let the length of the basement be x. then
12+12+x=30
x=30-24=6

$semi \: perimeter(s) =perimeter \div 2$

$= \frac{30}{2} = 15$
$area = \sqrt{s(s - a)(s - b)(s - c)}$

$= \sqrt{15(15 - 12)(15 - 12)(15 - 6)}$

$= \sqrt{15 \times 3 \times 3 \times 9}$
$= 9 \sqrt{15}$

:-)hope it helps u.