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Area of a triangle is the region covered by its three sides in a plane. Area of a triangle is equal to half of product of its base and height. Find the area using heron's formulas and SAS condition, with examples at BYJU'S.
Area of a Triangle tutorial. Pictures, examples and many practice problems on how to find the area of a triangle from its base and its height.
How to calculate the area of a triangle. In order to calculate the area of a triangle: Identify the base and perpendicular height of the triangle. Write the area formula. Substitute known values into the area formula. Solve the equation. Write the answer, including the units.
Area of the triangle is a basic geometric concept that calculates the measure of the space enclosed by the three sides of the triangle. The formulas to find the area of a triangle include the base-height formula, Heron’s formula, and trigonometric methods.
Area of a Triangle Formula. The area of a triangle [latex]A[/latex] is half the product of its base [latex]b[/latex] and its height [latex]h[/latex]. The height of a triangle is also known as the altitude. This formula works only if the base is perpendicular to the height.
The basic formula to find the area of a triangle is, area of triangle = 1/2 (b × h); where 'b' is the base and 'h' is the height of the triangle. However, there are other formulas that are used to find the area of a triangle which depend upon the type of triangle and the known dimensions.
The area of a triangle is a measure of the region (in the plane) enclosed within the triangle. For example, the area of the triangle above is the quantity that gives an accurate measure of the yellow region.
Understanding how to calculate the area of a triangle is essential for accurate material estimation, spatial planning, and construction, making it a fundamental skill in both academic and practical applications. First, determine the base and the height of the triangle.
The area of a triangle is equal to half the product of two sides times the sine of the included angle. This is also known as the sine rule for the area of a triangle. By considering sin A and sin B in a similar way, we obtain \(Area = \frac{1}{2}bc\sin A\) or \(Area = \frac{1}{2}ac\sin B\)
Example 1: Find the area of the triangle whose base is 8 inches long and height is 12 inches. Solution: Area of triangle = \ (\frac {1} {2}\times \text {b}\times \text {h}\) = \ (\frac {1} {2}\) (8) (12) [Substitute values of b and h] = \ (\frac {1} {2}\) (96) [Multiply]