Facts for Kids

🔺 The area ( A ) of a triangle can be calculated using the formula ( A = rac{1}{2} imes ext{base} imes ext{height} ).

📏 In a right triangle, the area can also be expressed as ( A = rac{1}{2} imes a imes b ), where ( a ) and ( b ) are the legs of the triangle.

📐 For an equilateral triangle, the area can be computed using ( A = rac{sqrt{3}}{4} imes s^2 ), where ( s ) is the length of a side.

🧮 The formula for the area can also be represented using Heron's formula as ( A = sqrt{s(s-a)(s-b)(s-c)} ), where ( s ) is the semi-perimeter.

✨ The semi-perimeter ( s ) is calculated as ( s = rac{a+b+c}{2} ) in Heron's formula.

📉 The altitude of a triangle must be drawn perpendicularly from a vertex to the opposite side to correctly use the area formula.

📊 The area of a triangle is independent of the triangle's orientation; it only depends on the base and height measurements.

💡 For two triangles with equal bases and heights, their areas will also be equal, regardless of their shapes.

🏗️ The area can also be determined if all three sides are known using the formula derived from Heron’s formula.

🌐 A triangle's area can also be derived using coordinates of its vertices with the formula ( A = rac{1}{2} |x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2)| ).