Answer:
The area of a triangle can be calculated using the formula:
Area = 1/2 * base * height
In the given right-angled triangle ABC, we know that the angle of the top vertex (A) is 45 degrees and the angle of the right vertex (C) is 45 degrees. This means that the triangle is an isosceles right triangle, where the two legs are congruent.
Let's label the points: A, B, and C. The length of AC is given as 24 cm.
Since the triangle is isosceles, the length of AB is also 24 cm.
To find the area of the triangle, we need to find the base and height.
Since the triangle is right-angled, one of the legs (AB or BC) can be considered as the base, and the other leg will be the height.
In this case, we can consider AB as the base and BC as the height.
Since the triangle is isosceles, the base and height are equal. Therefore, the base (AB) is 24 cm and the height (BC) is also 24 cm.
Now we can calculate the area using the formula:
Area = 1/2 * base * height
Area = 1/2 * 24 cm * 24 cm
Area = 12 cm * 24 cm
Area = 288 cm^2
Therefore, the area of the triangle is 288 square centimeters
Explanation: