To calculate the perimeter of the isosceles triangle, we need to know the lengths of all three sides. We already know the base of the triangle is 24 cm, but we need to find the lengths of the two equal sides, and we can use the area information to help with that.

Step 1: Area Formula of Triangle

The area $A$ of a triangle can be calculated using the formula: $A = \frac{1}{2} \times \text{base} \times \text{height}$ Given that the base $b = 24$ cm, the area is also provided as a number of square centimeters (please provide the area if you know it).

Step 2: Finding the Height

Since the triangle is isosceles, the height splits the base into two equal parts. So, each half of the base will be: $\frac{\text{base}}{2} = \frac{24}{2} = 12 \, \text{cm}$

Using the area formula, we can solve for the height $h$: $A = \frac{1}{2} \times 24 \times h$ $A = 12h$ So, $h = \frac{A}{12}$

Step 3: Finding the Length of the Equal Sides

To find the length of the equal sides $s$, we can use the Pythagorean theorem. The height divides the triangle into two right-angled triangles, where the base is 12 cm, the height is $h$, and the hypotenuse is the equal side $s$.

Using the Pythagorean theorem: $s^2 = 12^2 + h^2$ $s^2 = 144 + h^2$ $s = \sqrt{144 + h^2}$

Step 4: Perimeter of the Triangle

The perimeter $P$ of the isosceles triangle is the sum of all three sides: $P = 2s + 24$ You will substitute the value of $s$ that you calculated above.

Once you provide the area, we can proceed with the specific calculations. Let me know if you have the area value or need any further clarification!