Answer:
Let's denote the length of the equal sides of the isosceles triangle by "x". Then the perimeter of the triangle can be expressed as:
Perimeter = 2x + 9
But we also know that the perimeter of the triangle is 25cm, so we can set these two expressions equal to each other and solve for x:
2x + 9 = 25
2x = 16
x = 8
Therefore, the length of each of the equal sides is 8cm. Now, we can use the formula for the area of a triangle:
Area = (base × height) / 2
Since the triangle is isosceles, we know that the height is also the perpendicular bisector of the base, dividing it into two equal parts of length 4.5cm each. Now we can find the height of the triangle using the Pythagorean theorem:
h² + 4.5² = 8²
h² + 20.25 = 64
h² = 43.75
h ≈ 6.61
Substituting these values into the formula for the area of the triangle, we get:
Area = (9 × 6.61) / 2
Area ≈ 29.76 cm²
Therefore, the area of the isosceles triangle is approximately 29.76 cm².