Area of Scalene Triangle

We know that a triangle is a closed figure having 3 sides and 3 angles. Triangles come in a variety of shapes and sizes. All three sides of some of these triangles are the same length, two sides are the same length, and all three sides are different lengths in others.

A scalene triangle is one in which all three sides are unequal in length and all three angles are measured differently. 

The area between the scalene triangle’s boundaries is the entire area of the scalene triangle. A scalene triangle is a form of triangle in which all three sides of the triangle have distinct lengths and the angels have various measurements. Despite the fact that all of the angles in a scalene triangle are different, the sum of the triangle’s interior angles is still 180 degrees.

AREA OF ISOSCELES TRIANGLE:-

The area of a scalene triangle is equal to the amount of space covered by a flat surface within the triangle. It’s counted in the number of square units (square cm, square inches, square feet, square m, etc.).

The area occupied by the scalene triangle within its boundary is calculated using the area of the scalene triangle formula. Half of the product of the base and the height of the triangle yields the area of the scalene triangle. We can find the area of the scalene triangle by using the length of the side using heron’s formula.

CALCULATION OF AREA OF SCALENE TRIANGLE:-

As a triangle includes six quantities, three sides and three angles, the area of a triangle is determined using several formulas based on the triangle’s known quantities.we can calculate the area of scalene triangle by using the following known quantity:-

• The length of one side and the angle at which it is perpendicular to the opposite angle.
• The measurements of each of the three sides

Area when base and altitude are known:-

A scalene triangle with any side as the basis ‘b’ and height ‘h’ (an altitude on that base) has an area of

Area of scalene triangle:- ½×b×h.

Area of scalene triangle using heron’s formula:-

Heron of Alexandria was the first to reveal Heron’s formula. It’s used to calculate the area of various triangles, including equilateral, isosceles, and scalene triangles, as well as quadrilaterals. In this lesson, we’ll learn how to use Heron’s formula to calculate the area of triangles and quadrilaterals.

As per Heron’s formula, the value of the area of any triangle having lengths, a, b, c, perimeter of the triangle, P, and semi-perimeter of the triangle as S=(a+b+c)/2. Then the 

Area:-√S(S-a)(S-b)(S-c) sq. Units

STEPS TO DETERMINE AREA:-

The following are the steps to use Heron’s formula to calculate the area:

Step 1 :- Calculate the perimeter of the triangle given.

Step 2:- By halving the perimeter, you may find the semi-perimeter.

Step 3:- Using Heron’s formula √(s(s – a)(s – b)(s – c)), calculate the triangle’s area.

Step 4:- After you’ve found the value, add the unit at the end (For example, m², cm², or in²).

AREA OF TRIANGLE WHEN TWO SIDES AND ANGLE ARE INCLUDED:-

When the lengths of its two sides and the included angle are known, the area of the scalene triangle can be calculated.

1. The area of a triangle is equal to (1/2) bc sin A when two sides b and c and the included angle A are known.
2. The area of the triangle is Area = (1/2) ac sin B when the sides a and c and the included angle B are known.
3. The area of the triangle is Area = (1/2) ab sin C when the sides a and b and the included angle C are known.

PROPERTIES OF SCALENE TRIANGLE:-

The scalene triangle has a number of essential qualities that are given below:

• There are no equal sides to it.
• It doesn’t have any equal angles.
• It doesn’t have a symmetry line.
• There is no symmetry in the points.
• Inside this triangle, the angles can be acute, obtuse, or right.
• The center of the circumscribing circle will lie inside a triangle if all of the triangle’s angles are less than 90 degrees (acute).
• The circumcenter of a scalene obtuse triangle will be outside the triangle.
• A scalene triangle can have an obtuse, acute, or right-angled angle to it.

Example 1:- Find the area of the triangle whose base is 8 cm and altitude is 4 cm.

Answer:- We have the base of the triangle(b)= 8 cm 

                      And the height of the triangle(h)= 4 cm

                 Area of the triangle= ½×b×h

                                                    =½×8×4=16 cm².

Example 2:- Find the area of the scalene triangle whose length of sides are 3 cm , 4 cm and 5 cm.

Answer:- We have a= 3 cm , b = 4 cm ,  c = 5 cm.

                S= (a+b+c)/2= (3+4+5)/2= 6 cm.

                Area of the triangle= √S(S-a)(S-b)(S-c)

                                                  =√6(6-3)(6-4)(6-5)

                                                  =√6×3×2 = √36 = 6 cm².

CONCLUSION:-

A scalene triangle is one in which all three sides are unequal in length and all three angles are measured differently. A scalene triangle is a form of triangle in which all three sides of the triangle have distinct lengths and the angels have various measurements. Despite the fact that all of the angles of a scalene triangle are different, the sum of all of the triangle’s interior angles is 180 degrees.