Answer: the area of the isosceles triangle is 27 square centimeters
Explanation:
Since the triangle has a perimeter of 30 cm and two of its sides are 12 cm each, we can subtract twice the length of one of the equal sides from the perimeter to get the length of the third side:
Third side = Perimeter - 2 x Length of equal side
= 30 cm - 2 x 12 cm
= 6 cm
Now that we know all three sides of the triangle, we can use Heron's formula to find its area. Heron's formula states that the area of a triangle with sides of length a, b, and c is given by:
Area = sqrt[s(s-a)(s-b)(s-c)]
where s is the semiperimeter, given by:
s = (a + b + c) / 2
In our case, the sides of the triangle are 12 cm, 12 cm, and 6 cm. Therefore, the semiperimeter is:
s = (12 cm + 12 cm + 6 cm) / 2
= 15 cm
Using Heron's formula, we can now find the area of the triangle:
Area = sqrt[15(15-12)(15-12)(15-6)]
= sqrt[15 x 3 x 3 x 9]
= 27 cm^2
Therefore, the area of the isosceles triangle is 27 square centimeters.