Final answer:
The area of a right-angled triangle with two equal sides and a hypotenuse of 12 cm is 36 square centimeters.
Step-by-step explanation:
The question pertains to finding the area of a right-angled triangle when the lengths of the two equal sides and the longest side (hypotenuse) are known. Since it is given that this is an isosceles right-angled triangle (two equal sides), the equal sides are also the base and height of the triangle. For an isosceles right-angled triangle, if the hypotenuse is 12 cm, each of the other two sides will be of length √(12² / 2) cm, which is approximately 8.49 cm.
Thus, using the formula for the area of a triangle, which is 1/2 × base × height, the area can be calculated as follows:
Area = 1/2 × 8.49 cm × 8.49 cm = 36 cm².
This means the area of the given right-angled triangle is 36 square centimeters.