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\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

Area of a Triangle

Ma’am, I have learnt how
to calculate the area of a Seema, it’s not difficult. We can use
rectangle and a square. the concept of ‘area of a rectangle’
But, I do not know how to find the area of a triangle. For
to find the area of a this, let us explore the relation
triangle. between a triangle and a rectangle.

Let us draw a rectangle on a piece of paper and cut the rectangle along one of its diagonals to get
two triangles.

Superimpose one triangle to another and
check whether the two triangles have the
same area.

Try this with more rectangles having
different dimensions. You can check this for a square as well.
Now, we can draw an inferences from this activity that the two obtained triangles have the same
area and the area of each triangle is half the area of the original rectangle. That is

1
Area of a triangle = × Area of a rectangle
2
Now, let us draw suitable triangles on a square grid paper to verify A B E
the above inferences and relationships observed.

By counting the unit squares enclosed in the figures, we find:
Area of rectangle ABCD = 20 sq. units

Area of triangle BCD = 10 sq. units

1 D C F
That means, area of triangle BCD = of area of rectangle ABCD
2
Now, find the area of the following and write your conclusion:

• Area of rectangle BEFC = ............... sq. units.
• Area of triangle BCF = ............... sq. units.

• Area of triangle BCF = ............... area of rectangle BEFC.
• Area of rectangle ABCD + Area of rectangle BEFC = Area of rectangle ............... .

• Area of triangle BCD + Area of triangle BCF = Area of triangle ............... .

189
189 P erimeter and Ar ea
Perimeter and Area