Understanding Triangle ABC
Triangle ABC is an isosceles triangle, characterized by having two equal sides. In this case, sides AB and AC are each 7.5 cm, while the base BC measures 9 cm.
Key Characteristics
- Isosceles Triangle: Triangle ABC has two equal sides (AB = AC = 7.5 cm).
- Base: The base BC is 9 cm long.
- Vertices: The vertices of the triangle are A, B, and C.
Calculating the Area
To find the area of triangle ABC, we can use the following steps:
1. Calculate the Height:
- Drop a perpendicular from point A to base BC, which we'll call point D.
- BD = CD = 4.5 cm (since BC = 9 cm and BD = CD in an isosceles triangle).
2. Use the Pythagorean Theorem:
- AD = sqrt(AB^2 - BD^2) = sqrt(7.5^2 - 4.5^2).
3. Area Formula:
- Area = 1/2 * base * height = 1/2 * BC * AD.
Conclusion
Triangle ABC, with sides measuring 7.5 cm and a base of 9 cm, showcases the unique properties of an isosceles triangle. By applying geometric principles, we can derive key measurements like area and height, further enhancing our understanding of its structure.