Two sides of an isosceles triangle are 22 cm and 61 cm . What is the area of the triangle, in \( \mathrm{cm}^{2} \) ? Twee sye van 'n gelykbenige driehoek is 22 cm cn 61 cm . Wat is die oppervlakte van die driehoek, in \( \mathrm{cm}^{2} \) ? \( \begin{array}{llll}\text { (1) } 671 & \text { (2) } 660 & \text { (3) } 576 & \text { (4) } 630 \\ \text { (5) Not enough information / Nie genoeg inligting nie } & \end{array} \)

We are given an isosceles triangle with two known side lengths 22 cm and 61 cm. Since a triangle must satisfy the triangle inequality, the only possibility is that the two equal sides are 61 cm and 61 cm, and the base is 22 cm. (A triangle with two sides of 22 cm and a base of 61 cm would not work because 22 + 22 = 44, which is less than 61.) Now, to find the area of the triangle, we can use two methods: Method 1: Altitude of the Triangle 1. Draw the altitude from the vertex opposite the base (which will be perpendicular to the base and bisect it). Since the base is 22 cm, half of it is 11 cm. 2. The altitude h can be found using the Pythagorean theorem:   h = √(61² – 11²)    = √(3721 – 121)    = √3600    = 60 cm 3. The area A is then:   A = (1/2) × base × height    = (1/2) × 22 × 60    = 11 × 60    = 660 cm² Method 2: Heron’s Formula 1. The sides of the triangle are 61, 61, and 22. The semi-perimeter s is:   s = (61 + 61 + 22) / 2    = 144 / 2    = 72 cm 2. The area A is given by:   A = √[s(s - 61)(s - 61)(s - 22)]    = √[72 × 11 × 11 × 50]    = √[72 × 121 × 50]    = √[3600 × 121]   (because 72×50 = 3600)    = √(3600) × √(121)    = 60 × 11    = 660 cm² Both methods give us the same area: 660 cm². Thus, the correct answer is: (2) 660