Area and Perimeter are the two important formulas in the basic theory of **Mensuration**. This article helps to learn the properties and types of triangles here. The two main concepts to measure the sides of the triangle are area and perimeter. There are different formulas to find the perimeter and area of the triangle.

A two-dimensional closed figure with three sides is called a triangle. Our main aim is to make the students understand the concept of Area and Perimeter of the Triangle. Learn how to calculate the area and perimeter of the triangle by using the below mentioned solved examples.

## What is the Area and Perimeter of the Triangle?

**Area:** Area is defined as the measure of the region occupied by the triangle. The units to measure the area of the triangle is square meters or square centimeters.

**Perimeter:** The perimeter is the measure of lengths of the triangle. The perimeter of the triangle is the sum of all the sides of the triangle. The units to measure the perimeter of the triangle is meters or centimeters.

### Area and Perimeter of the Triangle Formula

The area of the triangle is half of the base and height.

A = 1/2 × base × height

The perimeter of the triangle is the sum of three sides of the triangle.

P = a + b + c

### Area of Triangle with three sides (Heron’s Formula)

The Area of the triangle with three sides can be found using Heron’s Formula. There are two steps to find the area of the triangle using Heron’s Formula. The first step is to find the value of s (semiperimeter of the triangle) by adding all the three sides i.e, a, b, c, and dividing by 2. The next steps is to apply the semi-perimeter of the triangle with the main formula

s = (a+b+c)/2

A = √s(s-a)(s-b)(s-c)

### Types of Triangles

There are 4 types of triangles. They are:

- Equilateral triangle
- Isosceles triangle
- Scalene triangle
- Right triangle

### Properties of triangle

- The sum of three angles of the triangle is 180º
- A triangle has three sides, three vertices, and three angles.
- The sum of two lengths of the triangle is greater than the third side.
- The area of the triangle is half of the base and height.

### Worked Out Example Problems on Area of the Triangle

**1. Find the area of the triangle whose base is 10 cm and height is 11 cm?**

Solution:

Given,

b = 10 cm

h = 11 cm

Area of triangle = 1/2 × b × h

A = 1/2 × 10 cm × 11 cm

A = 5 cm × 11 cm

A = 55 sq. cm

Therefore the area of the triangle is 55 sq. cm

**2. Find the missing length whose perimeter is 36cm and two sides of the triangles are 14 cm?**

Solution:

Given,

a = 14 cm

b = 14 cm

c = x

P = 36 cm

Perimeter of the triangle = a + b + c

36 cm = 14 cm + 14 cm + x

36 cm = 28 cm + x

x = 36 cm – 28 cm

x = 8 cm

Thus the length of third side of the triangle is 8 cm.

**3. Given a = 10m, b = 12m and c = 13m. Find the perimeter of the scalene triangle?**

Solution:

Given,

a = 10m

b = 12m

c = 13m

Perimeter of the triangle = a + b + c

P = 10m + 12m + 13m

P = 35m

Thus the perimeter of the scalene triangle is 35 meters.

**4. The area of the triangle is 144 cm² and the base is 12 cm. Find the height of the triangle?**

Solution:

Given,

The area of the triangle is 144 cm²

base = 12 cm.

Area of triangle = 1/2 × b × h

144cm² = 12 cm × h

h = 144cm²/12cm

h = 12 cm

Thus the height of the triangle is 12 cm.

**5. Find the area of the isosceles triangle whose base is 7m and height is 10m?**

Solution:

Given,

b = 7m

h = 10m

Area of the isosceles triangle = 1/2 × b × h

A = 1/2 × 7m × 10m

A = 7m × 5m

A = 35 sq. m

Thus the area of the isosceles triangle is 35 sq. m.

**6. Find the semi perimeter of the triangle whose sides of the triangle a = 5cm, b = 6cm, and c = 7cm using Heron’s formula?**

Solution:

Given,

a = 5cm

b = 6cm

c = 7 cm

s = (a+b+c)/2

s = (5cm + 6cm + 7 cm)/2

s = 18cm/2

s = 9 cm

Therefore the semi-perimeter of the triangle is 9cm.

**7. Find the area of the triangle with three given sides a = 1m, b = 3m, c = 4m?**

Solution:

Given,

a = 2m

b = 3m

c = 4m

First, we need to find the semiperimeter of the triangle.

s = (a+b+c)/2

s = (1 + 3 + 4)/2

s = 8/2

s = 4m

Now find the area of the triangle with three sides

A = √s(s-a)(s-b)(s-c)

A = √4(4-1)(4-3)(4-4)

A = √4(3)(1)(0)

A = 0

### FAQs on Area and Perimeter of the Triangle

**1. What is the formula for area and perimeter of the triangle?**

The area of the triangle is 1/2 × b × h

The perimeter of the triangle is a + b + c

**2. How to calculate the perimeter of the triangle?**

We can calculate the perimeter of the triangle by adding all three sides.

P = a + b + c

**3. What is the relationship between the area and perimeter of the triangle?**

The area is half of the base and height whereas the perimeter is the sum of all the three sides of the triangle.