Area of triangle

Chapter 11 Class 7 Perimeter and Area
Concept wise

Let us take triangle ABC

Let there be another triangle which is exactly same as ∆ABC

If we join both these triangles

We get a parallelogram ABCD

So, two equal triangles form a parallelogram

Now,

Area of parallelogram = Base × Height

Area of ∆ABC + Area of ∆DEF = b × h

Since both triangles are same,

their area will be equal

Area of ∆ABC + Area of ∆ ABC = b × h

2 Area of ∆ABC = b × h

Area of ∆ABC = b × h

Area of ∆ABC = 1/2 × b × h

So, our formula is

Area of triangle = 1/2 × b × h

For right angled triangle ∆ABC

Height = h = AB

Base = b = BC

So,

Area of ∆ABC = 1/2 × b × h

= 1/2 × AB × BC

Here,

base is any side of triangle

& height is perpendicular from opposite  vertex to the base

Let’s take some examples

Find area of Δ ABC

In ∆ABC,

= 4 cm

Base = b = BC

= 5 cm

So,

Area of ∆ABC = 1/2 × b × h

= 1/2 × 5 × 4

= 5 × 2

= 10 cm 2

∴ Area of ∆ABC is 10 cm 2

Note: Here, height is outside the triangle

Find area

In ∆ABC,

= 3 cm

Base = b = BC

= 4 cm

So,

Area of ∆ABC = 1/2 × b × h

= 1/2 × 4 × 3

= 2 × 3

= 6 cm 2

∴ Area of ∆ABC is 6 cm 2

Find area

In ∆ABC,

Height = h = BE

= 4 m

Base = b = AC

= 8 m

So,

Area of ∆ABC = 1/2 × b × h

= 1/2 × 8 × 4

= 4 × 4

= 16 m 2

∴ Area of ∆ABC is 16 m 2

Find area

In ∆ABC,

Height = h = BE

= 3 m

Base = b = AC

= 3 m

So,

Area of ∆ABC = 1/2 × b × h

= 1/2 × 3 × 3

= 1/2 × 9

= 9/2

= 4.5 m 2

∴ Area of ∆ABC is 4.5 m 2

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.