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Calculating the area of a triangle generally applies to various types such as right-angled, isosceles, equilateral triangles. However, in specific cases, applying specific formulas will be quicker. Here are specific cases to help you apply the simplest and fastest solutions to your geometry problems.
Formula for calculating the area of a triangle in grade 10.
HOW TO CALCULATE THE AREA OF A TRIANGLE
+ Calculating the area of a regular triangle: A regular triangle is a triangle with three sides of equal length.
Formula: S = 1⁄2 a.h (where a is the length of the base, h is the height corresponding to the base)
The area of a regular triangle is half the product of the height multiplied by the base length.
Example: Calculate the area of a triangle with side a = 10 cm and corresponding height denoted as h = 12 cm.
Solution:
Applying the formula for the area of a regular triangle, we have: S = 1⁄2 a.h = 1⁄2 x 10 x 12 = 60 cm2
The answer to the problem is 60 cm2
+ Calculating the area of a right-angled triangle: A right-angled triangle has one angle measuring 90 degrees.
Formula: S = 1⁄2 a.b (where a and b are the two sides forming the right angle)
The area of a right-angled triangle is half the product of its two sides forming the right angle. In the case of an isosceles right-angled triangle, where both sides are equal, the formula becomes S = 1⁄2 a2 with a being the length of the sides forming the right angle.
Example: Consider right-angled triangle ABC with a right angle at B. If AB is half the length of BC and measures 3 cm, calculate the triangle's area.
Solution:
Given that one side of the right angle AB = 3 cm, and AB is half the length of BC, we find BC = 2 x AB = 2 x 3 = 6 cm.
Applying the formula for calculating the area of a right-angled triangle, we get: S = 1⁄2 a.b = 1⁄2 x 3 x 6 = 9 cm2
+ Calculating the area of an isosceles triangle: An isosceles triangle has 2 equal sides.
Formula: S = 1⁄2 a.h (where a is the length of the base, h is the height corresponding to the base)
The area of an isosceles triangle is half the product of the height multiplied by the base, using the same formula as for a regular triangle in this case.
Example: For isosceles triangle ABC with the base at B, let H be the midpoint of side BC, AC = 9 cm, BH = 12 cm. Calculate the area of triangle ABC.
Solution:
Given the problem with height BH = 12 cm and base AC = 9 cm.
Applying the formula for area calculation, we have: S = 1⁄2 a.h = 1⁄2 x 12 x 9 = 54 cm2
+ Calculating the area of an equilateral triangle: An equilateral triangle has 3 equal sides and 3 equal angles, each measuring 60 degrees.
Formula: S = a2√3/4 (where a is the length of one side of the triangle)
The area of an equilateral triangle is the square of one side multiplied by the square root of 3, divided by 4.
Example: Calculate the area of an equilateral triangle with a side length of 5 cm.
Solution:
Applying the formula for the area of an equilateral triangle, we get the area directly:
S = a2√3/4 = 25√3/4 = 10.825 cm2
Here are specific cases of triangles and the simplest methods to calculate their areas. Additionally, for problems providing triangle sides and angles, you can apply trigonometric formulas to calculate the triangle area, which will be shared in upcoming articles by Mytour.vn.
https://Mytour.vn/cach-tinh-dien-tich-tam-giac-25350n.aspx
We also update and share formulas for calculating the area of a rectangle in our articles, providing students with convenient tools for math problems.
