Question

Find the area of an isosceles triangle with perimeter 38 cm and each of its equal sides 12 cm.



Please answer fast it’s urgent please

Answer 1

Answer:

66.74

Hope it helps you dude

Answer 2

Area of an isosceles triangle is $35\sqrt{3} cm^{2}$

Step-by-step explanation:

• We are given,

Perimeter of an isosceles triangle is 38 cm.

Equal sides of isosceles triangle (a) is 12 cm.

We have to find the third side of an isosceles (b) and the area of triangle.

• Formula used,

Perimeter of an isosceles triangle $=(2*a)+b$

Area of an isosceles triangle $=\frac{1}{2}*b*h$

h is the height of isosceles triangle and to calculate height (h) we use Pythagoras theorem of right angled triangle.

$h=\sqrt{a^{2}-\frac{b^{2} }{4} }cm$

• Calculation for third side of isosceles triangle (b),

We have the value of $a=12cm$ and for finding the 'b' we use perimeter formula and get,

Perimeter of an isosceles triangle $=(2*a)+b$

                                                    $38=(2*12)+b$

                                                     $38=24+b$

                                                     $b=14cm$

We get the third side of isosceles triangle $=b=14cm$

• Calculation for height (h),

We have $a=12cm$  and  $b=14cm$ by using the values of a and b we get height (h) as,

$h=\sqrt{a^{2}-\frac{b^{2} }{4} }$

  $=\sqrt{(12)^{2}-\frac{(14)^{2} }{4} }$

  $=\sqrt{144-\frac{196}{4} }$

   $=\sqrt{144-69}$

  $= \sqrt{75}$

   $=\sqrt{25*3}$

   $=5\sqrt{3}cm$

We get height of isosceles triangle $=h=5\sqrt{3}cm$

• Calculation for area of Isosceles triangle,

We have  $b=14cm$  and  $h=5\sqrt{3}cm$ by using these values we will get area of isosceles triangle,

Area of an isosceles triangle $=\frac{1}{2}*b*h$

                                               $=\frac{1}{2}* 14*5\sqrt{3}$

                                                 $=35\sqrt{3}cm^{2}$

The area of an isosceles triangle is $35\sqrt{3}cm^{2}$.