The length of the base of an isosceles triangle is 24 cm and the length of each equal side is 13 cm. The area of the triangle is :

1. 60 cm²

2. 120 cm²

3. 156 cm²

4. 164 cm²

Given,

Length of each equal side (a) = 13 cm and base (b) = 24 cm.

By formula,

$\Rightarrow \text{Area of isosceles triangle} = \dfrac{1}{4}b \sqrt{4a^2 - b^2} \\[1em] = \dfrac{24}{4} \sqrt{4(13)^2 - 24^2} \\[1em] = 6 \sqrt{4 × 169 - 576} \\[1em] = 6 \sqrt{676 - 576} \\[1em] = 6 \sqrt{100} \\[1em] = 6 × 10 \\[1em] = 60 \text{ cm}^2.$

Hence, option 1 is the correct option.