Table of Contents

Last modified on August 3rd, 2023

In geometry, a triangle is a plane figure that is enclosed by three line segments.

- Side
- Angle
- Vertex

- The sum of all the angles of a triangle is equal to 180°
- The sum of the lengths of any two sides of a triangle is greater than the length of the third side
- The difference between any two sides of a triangle is less than the length of the third side
- An exterior angle of a triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of the triangle

It is the total space enclosed by the triangle. The formula is given below:

**Problem:** Finding the area of a triangle when the **BASE** and **HEIGHT** are known

**Find the area of a triangle whose base is 6 cm and height is 4 cm?**

Solution:

As we know,**A****= ½ (****b**** × ****h****)**

= ½ (6 × 4) cm

= 12 cm^{2}

**Problem:** Finding the area of a triangle when only **SIDES** are known

**Find the area of a triangle whose three sides are 3 cm, 4 cm, and 5 cm.**

Solution:

Here we will use the Heron’s formula,**A**** = √****s****(****s****–****a****)(****s****–****b****)(****s****–****c****)**, where *s* = ½ (*a*+*b*+*c*)

In this triangle, *s* = ½ (3 cm + 4 cm+ 5 cm) = 6 cm

Since, *A*= √*s*(*s*–*a*)(*s*–*b*)(*s*–*c*)

= √6(6-3)(6-4)(6-5)

= √36

= 6 cm^{2}

It is the distance covered around the edges of a triangle or simply the length of the boundary covered. The formula is given below:

**Find the perimeter of a triangle whose three sides are 4 cm, 6 cm, and 8 cm**

Solution:

As we know,**P**** = ****a ****+ ****b**** + *** c*, where a, b, c are the measure of three sides

= 4 cm + 6 cm + 8 cm

= 18 cm

Triangles are classified into two groups: **based on sides**, 1) scalene, 2) isosceles, and 3) equilateral triangles; **based on angles**, 1) acute angle, 2) obtuse angle, and 3) right or right-angled triangles.

The differences between the types are given below:

Apart from the above three types, there is **Equiangular Triangle** with all three internal angles equal to 60° and, thus having all sides equal, similar to an Equilateral Triangle

- Triangle Worksheets
- Congruent Triangles Worksheets
- Special Right Triangles Worksheets
- Special Triangles Worksheets
- Similar Triangles Worksheets
- Area of a Triangle Worksheets
- Area of Triangles and Parallelograms Worksheets
- Area of Triangles and Trapezoids Worksheets
- Area and Perimeter of Triangles Worksheets
- Angles in a Triangle Worksheets
- Classifying Triangles Worksheets
- Isosceles and Equilateral Triangles Worksheets
- Right Triangle Worksheets
- Right Triangle Trigonometry Worksheets
- Triangle Sum Theorem Worksheets
- Midsegment of a Triangle Worksheets
- Triangle Inequality Theorem Worksheets
- Special Segments in Triangles Worksheets
- Triangle Proportionality Theorem Worksheets
- Centers of Triangles Worksheets
- Constructing Triangles Worksheets

- Further Reading
- Scalene Triangle
- Isosceles Triangle
- Equilateral Triangle
- Acute angled Triangle
- Obtuse angled Triangle
- Right triangle Triangle
- Special Right Triangles
- Congruent Triangles
- Altitude of a Triangle
- Similar Triangles
- Median of a Triangle
- Triangle Inequality Theorem
- Centroid of a Triangle
- Triangle Sum Theorem
- Incenter of a Triangle
- Vertices of a Triangle
- Hypotenuse of a Triangle
- Isosceles Triangle Theorem
- Exterior Angle of a Triangle
- Midsegment of a Triangle
- Base of a Triangle
- Perpendicular Bisector of a Triangle
- Angle Bisector of a Triangle

Last modified on August 3rd, 2023

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Thank you.

Rubaet Alam Rumon

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