Scalene Triangle
A scalene triangle is a type of triangle with unequal sides as well as three angles of different values. However, the sum of the interior angles of a scalene triangle is same as that of other triangles, that is, 180°.
Difference Between Scalene, Isosceles and Equilateral Triangles
Scalene triangle | Isosceles triangle | Equilateral triangle |
|---|---|---|
None of the edges are equal in length. | Two edges are equal in length | All three edges are equal in length. |
None of the angles are equal. | Two of the angles are equal. | All three angles are equal. |
Angles may be acute, obtuse or right angles. | Equal angles are acute. | Each angle measures 60°. |
Area of a Scalene Triangle
Area is a region occupied by the boundary of a figure. Here, the region covered by the edges of a scalene triangle is called the area of the scalene triangle. Area is measured in square units like square centimeters, square feet, square inches or square yards.
To calculate the area of a triangle we must have:
- An edge length (\(b \)) called base
- Measurement of an altitude (\(h \)) drawn on to the base from the opposite vertex
The formula for the area of a scalene triangle is, A = \(\frac{1}{2}~\times~b~\times~h \) square units.
So, area of triangle ABC = \(\frac{1}{2}~\times~AC~\times~BD \)
Perimeter of a Scalene Triangle
The perimeter of any figure is the total length of its boundary. When referring to a scalene triangle, all three edges(or sides)are not equal. So we add the length of the three sides to get the perimeter. The perimeter is measured in units like centimeters, meters, miles, feet, inches or yards.
Let’s suppose the measure of AB is a , BC is b and CA is c.
The perimeter of triangle ABC = Sum of all its three sides
Perimeter of ABC = AB + BC + CA
Perimeter of ABC = (a + b + c) units
Rapid Recall
- Area scalene triangle, A = \(\frac{1}{2}~\times~b~\times~h \) square units
- Perimeter of scalene triangle, P = (a + b + c) units
Solved Examples
Example 1: The base length of a triangle is 20 inches and height is 10 inches. Find the area of the given triangle.
Solution :
A = \(\frac{1}{2}~\times~b~\times~h \) Write the formula for the area of a triangle
A = \(\frac{1}{2}~\times~20~\times~10 \) Substitute 20 for b and 10 for h
A = \(\frac{200}{2} \) Multiply
A = 100 Divide
So, the area of the given triangle is 100 square inches.
Example 2: Find the altitude of a triangle whose base length is 20 yards and area is 120 square yards.
Solution :
A = \(\frac{1}{2}~\times~b~\times~h \) Write the formula for the area of a triangle
120 = \(\frac{1}{2}~\times~20~\times~h \) Substitute 120 for A and 20 for b
120 = \(10~\times~h \) Divide 20 by 2
\(\frac{120}{10} \) = \(\frac{10~\times~h}{10} \) Divide each side by 10
12 = \(h \)
Therefore, the altitude of the triangle is 12 yards.
Example 3: Find the perimeter of the given triangle.
Solution:
P = a + b + c Write the formula for the perimeter of a triangle
P = 13 + 5 + 10 Substitute 13 for a and 5 for b and 10 for c
P = 28 Add
So, the perimeter of the given triangle is 28 millimeters.
Example 4: Hazel created a triangular shape by pasting leaves on a sheet of cardboard. One of the altitude measures 15 centimeters and the total area covered by the leaves is 90 square centimeters. Find the corresponding base.
Solution:
A = \(\frac{1}{2}~\times~b~\times~h \) Write the formula for the area of a triangle
90 = \(\frac{1}{2}~\times~15~\times~h \) Substitute 90 for A and 15 for h
\(90~\times~2 \) = \(2~\times~\frac{1}{2}~\times~15~\times~h \) Multiply both side by 2
180 = \(15\times~h \) Solve
\(\frac{180}{15} \) = \(\frac{15~\times~h}{15} \) Divide each side by 15
12 = \(h \) Solve
Hence, the corresponding base length is 12 centimeters.
A triangle with three different sides is called a scalene triangle.
Yes, a scalene triangle may be an acute, right angled or even an obtuse angled triangle.
The sum of interior angles of all kinds of triangles is 180°.
The area of a scalene triangle is calculated with the formula in which half is multiplied by the base length and this is multiplied by the height. Area is always expressed in square units.
The sum of all the exterior angles of all kinds of triangles is 360°.