The three triangles meaning and they are given as follows,
Equilateral triangle:
An Equilateral triangle is a triangle where all the three sides are equal in length.
Area of an equilateral triangle = s^{2} √`4/3` square units
Perimeter of equilateral triangle = 3s units
Isosceles triangle:
An Isosceles triangle is a triangle where two sides are equal and one side is different.
Area of an isosceles triangle =`1/2` b x h
Perimeter of isosceles triangle = 2 (slant height) x base units
Scalene triangle:
A scalene triangle is a triangle where all the three sides are different in length.
Area of a scalene triangle = √s(s-a)(s-b)(s-c)
Where, s = `(a + b + c)/2`
Example 1:
Find the area and perimeter of a meaning equilateral triangle whose side length is equal to 6 centimeter.
Solution:
Area of an equilateral triangle = s^{2} `sqrt(3/4)` square centimeter
= 6^{2}`(sqrt3/4)`
= 36 × 1.732/4
= 15.58 square centimeter
Perimeter of equilateral triangle = 3s
= 3 × 6
= 18 centimeter
Example 2:
What is the area and perimeter of the triangle shown in the given figure ?
Area of the given triangle = `(1)/(2)` bh square units
Here, b = 9 and h = 4
Area =`(1)/(2)` × 9 × 4
= 9 × 2
= 18 square inches
To find the perimeter of this triangle, we need the slant height.
In the given diagram, the slant height of the triangle can be found using Pythagoras theorem
s^{2} = 4^{2} + 3^{2}
s^{2} = 16 + 9
s^{2} = 25
s = 5 inch
So the perimeter of this triangle = 2s × b
= 2 × 5 × 9
= 90 inches
Example 3:
Find the area and perimeter of a triangle with side lengths 2 ft, 4 ft, and 8 ft.
Solution:
The given dimensions represents a scalene triangle
so, the area of a scalene triangle =`sqrt(s(s-a)(s-b)(s-c))`
To find s,
s =`(a+b+c)/(2)`
Here, a = 2 ft, b = 4 ft, c = 8 ft.
s = 2+4+8/2
=14/2
s =7
area =`sqrt(7(7-2)(7-4)(7-8))`
=`sqrt(105/2)` =10.3ft^{2}
Perimeter of the triangle = 2 + 4 + 8
= 14 ft