Introduction to solve perfect triangles:
Triangles are three sided polygons. They are classified into equilateral triangles, isosceles, and right angled triangles. To solve perfect triangles, they should contain equal sides and angles. Perfect triangles include equilateral and right angled triangles. In triangles, we find the area, perimeter and the angles. Now we see some problems to solve perfect triangles.
Some basic properties of triangles and problems
Area formula = `1/2(b xx h)`
Perimeter formula = (a + b + c)
Interior angle = (n – 1) 180° and
Exterior angle = 360°/n
Where,
n – Number of sides
Problems to solve perfect triangles:
Example 1:
What is the area of an equilateral triangle, if it one of the side measures 5 cm?
Solution:
We know that, the equilateral triangle has same length in all the sides.
Formula to find the area of the triangle is given by,
Area =`1/2(b xx h)`
Here it has same breadth and length.
On substituting the side value, that is 5 in the areas formula,
Area =`1/2(5 xx 5)`
= `1/2(25)`
=12.5
Thus the area of the given equilateral triangle is 12.5 cm2.
Example 2:
Find the perimeter of the right angled triangle the sides are given as 3 cm, 6 cm, and 9 cm.
Solution:
We know the formula to find the perimeter of the given triangle
Perimeter = (a + b + c)
= (3 + 6 + 9)
= 18
Therefore the perimeter of the triangle is 18 cm.
Having problem with Sum of Exterior Angles Formula keep reading my upcoming posts, i will try to help you.
More problems to solve perfect triangles
Example 3:
Find the interior and exterior angles for the right angled triangle.
Solution:
Formula to find Interior angle = (n – 2) 180°
Here a right angled triangle has 3 sides. So n = 3
(n – 2) 180 = (3 – 2)180
= 180
The interior angle for a right angled triangle is 180°
Now to find the exterior angle, we know the formula as
`360/n = 360/3`
= 120
Hence the exterior angle is 120°.
Example 4:
A triangle has a total perimeter of 34 cm. If two sides are given as 12 cm and 14 cm, what is the length of the third side?
Solution:
Perimeter of the triangle is (a + b + c)
We know the two side’s length as 12 and 14.
So a = 12 cm and b = 14 cm
Let the third side be c.
12 + 14 + c = 34
26 + c = 34
Subtract by 26 on both sides, we get
26 – 26 + c = 34 – 26
c = 8
Therefore the third side’s length is 8 cm.
These are some example problems to solve perfect triangles.
Triangles are three sided polygons. They are classified into equilateral triangles, isosceles, and right angled triangles. To solve perfect triangles, they should contain equal sides and angles. Perfect triangles include equilateral and right angled triangles. In triangles, we find the area, perimeter and the angles. Now we see some problems to solve perfect triangles.
Some basic properties of triangles and problems
Area formula = `1/2(b xx h)`
Perimeter formula = (a + b + c)
Interior angle = (n – 1) 180° and
Exterior angle = 360°/n
Where,
n – Number of sides
Problems to solve perfect triangles:
Example 1:
What is the area of an equilateral triangle, if it one of the side measures 5 cm?
Solution:
We know that, the equilateral triangle has same length in all the sides.
Formula to find the area of the triangle is given by,
Area =`1/2(b xx h)`
Here it has same breadth and length.
On substituting the side value, that is 5 in the areas formula,
Area =`1/2(5 xx 5)`
= `1/2(25)`
=12.5
Thus the area of the given equilateral triangle is 12.5 cm2.
Example 2:
Find the perimeter of the right angled triangle the sides are given as 3 cm, 6 cm, and 9 cm.
Solution:
We know the formula to find the perimeter of the given triangle
Perimeter = (a + b + c)
= (3 + 6 + 9)
= 18
Therefore the perimeter of the triangle is 18 cm.
Having problem with Sum of Exterior Angles Formula keep reading my upcoming posts, i will try to help you.
More problems to solve perfect triangles
Example 3:
Find the interior and exterior angles for the right angled triangle.
Solution:
Formula to find Interior angle = (n – 2) 180°
Here a right angled triangle has 3 sides. So n = 3
(n – 2) 180 = (3 – 2)180
= 180
The interior angle for a right angled triangle is 180°
Now to find the exterior angle, we know the formula as
`360/n = 360/3`
= 120
Hence the exterior angle is 120°.
Example 4:
A triangle has a total perimeter of 34 cm. If two sides are given as 12 cm and 14 cm, what is the length of the third side?
Solution:
Perimeter of the triangle is (a + b + c)
We know the two side’s length as 12 and 14.
So a = 12 cm and b = 14 cm
Let the third side be c.
12 + 14 + c = 34
26 + c = 34
Subtract by 26 on both sides, we get
26 – 26 + c = 34 – 26
c = 8
Therefore the third side’s length is 8 cm.
These are some example problems to solve perfect triangles.
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