Question

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

Answer 1

perimeter of an isoceles triangle = a+b+c

                                             30cm= 12 +12+c

                                                    c=30-24=6cm

altitude of an isosceles triangle =root(a^2-b^2/4)

                                                     =11.62

area of an isosceles triangle .  =1/2 base *height

                                                    =1/2* 6*11.62

after solving we will get the answer

hope its helpful........

                                                   

Answer 2

First,let the third side be x.

It is given that the length of the equal sides us 12 cm and it's perimeter is 30 cm.

So,$30=12+12+x$

$⇒ 30 = 24 + x$

$⇒24 + x = 30$

$⇒ x= 30 - 24$

$⇒ x = 6$

So,the length of the third side is 6 cm.

Thus,the semi perimeter of the isosceles triangle (s) = 30/2 cm =15 cm

By using Heron's Formula,

Area of the triangle,

$= \sqrt{s(s - a)(s - b)(s - c)}$

$= \sqrt{15(15 - 12)(15 - 12)(15 - 6)} \: {cm}^{2}$

$= \sqrt{15 \times 3 \times 3 \times 9} \: {cm}^{2}$

$= 9 \sqrt{15} \: {cm}^{2}$