Question

An isosceles triangle has parameter 30 and each of equal side is 12 cm find the area of triangle​

Answer 1

Answer:

9√15 cm²

Step-by-step explanation:

perimeter = 30

one of equal side = 12

3rd side = 30 -12 -12

= 30 -24

= 6

half of third side = 3

height of isosceles triangle = √{12²-3²}

= √135 = 3√15

area = ½ × base × height

= ½ × 6 × 3√15

= 9√15

Answer 2

First,let the third side be x.

It is given that the length of the equal sides is 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,

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

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

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

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