The closed figure that is formed by least the number of line segments that is three line segments is known as a triangle. There are different types of triangles that are classifies on the basis of their sides and angles.
The triangles are that classified on the basis of lengths of the sides are
(i) Scalene
(ii) Isosceles
(iii) Equilateral
The triangles are that classified on the basis of the measures of their angles are
(i) Acute angled
(ii) Right angled
(iii) Obtuse angled
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Scalene Right Triangle
A scalene right triangle is a three sided figure in which all the three sides are different from each other and one of the angle measures 90 degrees.
Finding Area of a Triangle
Area of any three sided figure (triangle) is the region that is enclosed by the three sides of the figure. This can be found using different formula.
Formula : 1
Area = ½ * base * height
Where base is the side on which the altitude is drawn, height is the length of the altitude that is drawn on the corresponding base.
Example : 1
Find the area of the figure given below.
Solution :
In the given figure, we see that the altitude AD is drawn on to the side BC of the triangle. Therefore, Base = BC = 8 cm and height = AD = 3 cm.
We know, area = ½ * base * height
= ½ * 8 * 3
= ½ * 24
= 12 square cm
Example : 2
Find the area of a three sided figure whose sides lengths are 4 cm, 5 cm and 3 cm.
Solution :
Given, the three sides are
1st side = 4 cm
2nd side = 3 cm
3rd side = 5 cm
These three sides form a Pythagorean triplet. In which 4 cm and 3 cm are the lengths of the legs (that is the sides containing the right angle)
Therefore, Base = 4 cm and height = 3 cm.
We know, area = ½ * base * height
= ½ * 4 * 3
= ½ * 12
= 6 square cm
Formula : 2
If a, b and c are the lengths of all the sides of a triangle then its area is found using the formula
Area = square of root of [s(s – a)(s – b)(s – c)] square units
Where S is known as the semi perimeter and is found by sum of the side lengths divided by 2
Example : 3
Find the area of the triangle whose sides lengths are 6 cm, 7 cm and 9 cm
Solution :
Let a = 6 cm, b = 7 cm and c = 9 cm
Semi perimeter = (a + b + c)/2 = (6 + 7 + 9)/2 = 22/2 = 11 cm
s – a = 11 – 6 = 5
s – b = 11 – 7 = 4
s – c = 11 – 9 = 2
Area = √[s(s – a)(s – b)(s – c)] square units
Area = √[11(5)(4)(2)] square cm
Area = √[440] square cm
Area = 20.78 square cm
Example : 4
Find the area of the triangle whose sides lengths are 10 cm, 12 cm and 14 cm
Solution :
Let a = 10 cm, b = 12 cm and c = 14 cm
Semi perimeter = (a + b + c)/2 = (10 + 12 + 14)/2 = 36/2 = 18 cm
s – a = 18 – 10 = 8
s – b = 18 – 12 = 6
s – c = 18 – 14 = 4
Area = √[s(s – a)(s – b)(s – c)] square units
Area = √[18(8)(6)(4)] square cm
Area = √[3456] square cm
Area = 58.79 square cm
Formula : 3
If all the sides of the three sided figure are congruent to each other. Then such a figure is known as equilateral triangle.
Area = (√3/4)(a2) square units.
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