09:58 | 17/09/2024

What is the formula for calculating the area of an isosceles triangle in Vietnam?

Below are the formula for calculating the area of an isosceles triangle and some example excersises in Vietnam

What is the formula for calculating the area of an isosceles triangle in Vietnam?

The concept of an isosceles triangle is introduced for the first time in primary school (around grade 5).

A deeper understanding of the properties, theorems, and related problems of isosceles triangles is usually carried out in lower secondary school (grades 6, 7, 8).

Formula for calculating the area of an isosceles triangle

The general formula to calculate the area of any triangle (including isosceles triangles) is:

Area = (base x height) / 2

*In which:

- Base: The length of any side of the triangle.

- Height: The length of the perpendicular segment drawn from the opposite vertex to the base.

*Note: For isosceles triangles:

Special property: An isosceles triangle has two equal sides and two equal base angles. The height drawn from the vertex to the base is also the perpendicular bisector of the base.

*You can use one of the two following methods to calculate the area:

Method 1: Apply the general formula as above.

Method 2: Use the Pythagorean theorem to calculate the height, if the side length and base length are known, then apply the general formula.

*Note:

The height is always perpendicular to the base.

The base can be any side of the isosceles triangle.

For more complex problems, trigonometric formulas can be used to calculate the area.

*Note: The information is for reference only./.

Some simple exercises on calculating the area of an isosceles triangle

Type 1: Given the base and the height

Given an isosceles triangle ABC with BC = 10cm, height AH = 6cm. Calculate the area of triangle ABC.

An isosceles triangle has a base of 8cm, and the corresponding height is 5cm. Calculate the area of that triangle.

Type 2: Given the side and the base angle

Given an isosceles triangle ABC with AB = 5cm, angle B = 60°. Calculate the area of triangle ABC.

An isosceles triangle has a side of 8cm and a base angle of 45°. Calculate the area of that triangle.

Type 3: Given the sides of the triangle

Given an isosceles triangle ABC with AB = AC = 13cm, BC = 10cm. Calculate the area of triangle ABC.

An isosceles triangle has two equal sides of 10cm and a base of 12cm. Calculate the area of that triangle.

Type 4: Calculate the overlapping area

Given two equilateral triangles ABC and ABD with sides of 5cm, overlapping such that A, B, D are collinear. Calculate the overlapping area of the two triangles.

Given a square ABCD with a side of 8cm. Connecting the midpoints of the sides of the square forms a second square. Calculate the overlapping area of the two squares.

Type 5: Integrated problems

Given an isosceles triangle ABC with the height AH dividing the base BC into two segments BH = 4cm, HC = 6cm. Calculate the length of side AC and the area of triangle ABC.

Given an isosceles triangle ABC inscribed in a circle with center O and radius R = 5cm. Given angle BAC = 120°. Calculate the area of triangle ABC.

Note on guidance

- Draw a diagram: Always draw a diagram to visualize the problem.

- Apply the formula: Use the formula for calculating the area of a triangle: S = (base x height) / 2.

- Find the height: If the height is not known, use the Pythagorean theorem or trigonometric relationships in a right triangle to calculate it.

- Analyze the problem: For complex problems, break the problem down into simpler parts.

*Note: The information is for reference only./.

Formula for calculating the area of an isosceles triangle?

What is the formula for calculating the area of an isosceles triangle in Vietnam? (Image from the Internet)

From which grade in Vietnam is the formula for calculating the area of an isosceles triangle taught?

Based on Section III of the Appendix to the General Education Program in Mathematics issued under Circular 32/2018/TT-BGDDT for grade 5, the requirements are as follows:

For grade 5 Mathematics, in the Geometry and Measurement, plane figures and solid shapes section, the requirements are as follows:

Observe, recognize, and describe the shape and characteristics of some simple plane and solid shapes:

- Recognize trapezoids, circles, some types of triangles like acute triangles, right triangles, obtuse triangles, equilateral triangles.

For the General Education Program in Mathematics issued under Circular 32/2018/TT-BGDDT for grade 7, the more specific requirements are as follows:

Triangles. Congruent triangles. Isosceles triangles. The relationship between perpendicular lines and oblique lines. The concurrent lines of a triangle should ensure that students:

- Explain the theorem about the sum of the interior angles of a triangle being 180 degrees.

- Recognize the relationship between the lengths of the three sides in a triangle.

- Recognize the concept of congruent triangles.

- Explain the cases of congruence of two triangles, or two right triangles.

- Describe and explain the properties of isosceles triangles (for example: two equal sides; two equal base angles).

- Recognize the concepts: perpendicular line and oblique line; the distance from a point to a line. Explain the relationship between the perpendicular line and the oblique line based on the relationship between the sides and opposite angles in a triangle (opposite the larger angle is the longer side and vice versa).

- Recognize the perpendicular bisector of a segment and the basic properties of the perpendicular bisector.

Thus, the formula for calculating the area of an isosceles triangle may have been introduced by teachers from grade 5 and taught in the grade 7 mathematics program.

What are the overall objectives to ensure when teaching Mathematics to students in Vietnam?

Based on Section III of the Appendix to the General Education Program in Mathematics issued under Circular 32/2018/TT-BGDDT, when teaching Mathematics, the overall objectives should be as follows:

- Form and develop mathematical competencies including the following core components: mathematical reasoning and argumentation; mathematical modeling; mathematical problem-solving; mathematical communication; and ability to use mathematical tools and means.

- Contribute to forming and developing students' essential qualities and general competencies at levels appropriate to each subject or grade level as prescribed in the General Education Program.

- Have basic, essential general knowledge and skills in mathematics; develop the ability to solve integrated interdisciplinary problems between mathematics and other subjects such as Physics, Chemistry, Biology, Geography, Information Technology, Technology, History, Arts,...; create opportunities for students to experience and apply mathematics in practice.

- Have a relatively comprehensive understanding of the usefulness of mathematics for each related profession to serve as a basis for career orientation, and have sufficient minimum competencies to self-enquire about mathematics-related issues throughout life.

Download the General Education Program in Mathematics issued under Circular 32/2018/TT-BGDDT.

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