Table of contents | |
Definition | |
Properties | |
Perimeter of Triangle | |
Area of a Triangle | |
Area of Triangle Using Heron’s Formula |
"Have you ever wondered why bridges and buildings use triangles in their design? Triangles are known as the strongest shapes.
Let’s explore how this simple three-sided shape holds the key to stability and strength all around us!"
Hence,
Every shape in Maths has some properties which distinguish them from each other. Let us discuss here some of the properties of triangles.
The classification of triangles is based on two criteria
1. On the basis of length of the sides.
2. On the basis of measurement of the angles.
1. On the basis of length of the sides, triangles are classified into three categories
1. Scalene Triangle
A scalene triangle is a type of triangle, in which all the three sides have different side measures. Due to this, the three angles are also different from each other.
2. Isosceles Triangle
In an isosceles triangle, two sides have equal length. The two angles opposite to the two equal sides are also equal to each other.
3. Equilateral Triangle
An equilateral triangle has all three sides equal to each other. Due to this all the internal angles are of equal degrees, i.e. each of the angles is 60°
2. On the basis of measurement of the angles, triangles are classified into three categories
1. Acute Angled Triangle
2. Right Angled Triangle
3. Obtuse Angled Triangle
Area of triangle = Half of Product of Base and Height
Area = 1/2 × Base × Height
Example: Find the area of a triangle having base equal to 9 cm and height equal to 6 cm.
Sol: We know that Area = 1/2 × Base × Height
= 1/2 × 9 × 6 cm2
= 27 cm2
Example 1: If ABC is a triangle where AB = 3cm, BC=5cm and AC = 4cm, then find its perimeter.
Sol: Given, ABC is a triangle.
AB = 3cm
BC = 5cm
AC = 4cm
As we know by the formula,
Perimeter = Sum of all three sides
P = AB + BC + AC
P = 3+5+4
P = 12cm
Example 2: Find the area of a triangle having sides 5,6 and 7 units length.
Sol: Using Heron’s formula to find the area of a triangle-
Semiperimeter (s) = (a+b+c)/2
s = (5 + 6 +7)/2
s = 9
Now Area of a triangle = √[s(s-a)(s-b)(s-c)]
=√[9(9-5)(9-6)(9-7)]
=√ [9 × 4 × 3 × 2]
=√ [3 × 3 × 2 × 2 × 3 × 2]
=√ [32 × 22 × 3 × 2]
= 6√6 square units.
58 videos|112 docs|40 tests
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1. What is a triangle and how is it defined? |
2. What are the different types of triangles based on their sides? |
3. How do you calculate the perimeter of a triangle? |
4. What is the formula to find the area of a triangle? |
5. How does Heron’s formula work for finding the area of a triangle? |
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